The short answers to the question and its subquestions

• Q I couldn't find the source for this supposed anonymous chronicle.

It is in one manuscript of the so called 'continuation of Detmar's Lübeck chronicle'. Originally a single manuscript, now in Hamburg State Library (Ms Ham Cod Hist 33). Printed source editions — as long as they are young enough to include this late find — are reliable transcriptions of those, example linked and explained below.

• Q So what is the story behind this statement?

One manuscript in Lübeck recorded these numbers, a few years after that battle from 1410, in 1413. This single manuscript is itself not giving reliable numbers for the real number of participants, but then no contemporary source presents us anything like reliable numbers for the event.
The Lübeck source is mentioning the largest numbers, but all other sources either contradict each other as well, or at best give fragmentary information.
This one partial Lübeck manuscript is unique — among the Lübeck chronicles — in really covering the events in Grunwald/Tannenberg, all other versions of the Lübeck chronicle just leave them out.
This manuscript itself was lost for a long time and only rediscovered in the mid 19th century.
(And a Wikipedia author used this for the article cited from 2004 onward, which gained a [citation needed] label in 2008. Since none came forth this tidbit was then removed from the Wikipedia article in 2010.)

• Q Was there an actual chronicle that recorded these numbers?

Yes, the one just mentioned, the anonymous Lübeck City Chronicle in the continued tradition of Reading Master Detmar, who himself died around 1395. MS Ham Cod.hist. 33.

• Q Was it just an insane exaggeration?

It certainly is not a reliable real number. The anonymous scribe who wrote them embellished the numbers.

• Q Was it some type of typographical error? To clarify, I am asking whether there was typographical error in the aforementioned chronicle.

No. The scribe(s) wrote what you read today. More than 5 million soldiers on the side of Polish-Lithuanian forces. The manuscript is old, perhaps a few hands wrote it already originally. But then it was lost and only came to light again very late. Transcriptions for a source edition then made no errors in the relevant parts for this question, the transmission history is immaculate: this source gives the number quite explicitly as over 5 million soldiers.

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The chronicle in question, accurately transcribed into source editions

The relevant transcript from the one version of the 'continuation of Detmar's Lübeck chronicle Cronike van Lubeke' reads in one transcript version (from 1899, click to enlarge):

In desser schare hadde de konnigh van Krackowe 17 werve hundert dusent volkes; de konnigh Witolt van Lettowen 2800 dusent volkes. Ok was darto gekomen de konnigh van Neugarde mit den Rúsen; de brachten unmaten vele volkes ute Rusen to hulpe. In deme sulven heere was de keyser van Tatheren, de dar hadde 15 werve hundert dusent, dat men gissede, dat des volkes tosamende was viftich werve hundertdusent unde hundertwerve dusent. Hir is nu en vraghe, wat er spise was in deme weghe. Men antworde hir to: wat se vunden in deme weghe: perde, ezele, můlen, ossen, schape.

Notes, this is middle low German:

• werve — is an adverbial math construction, means times/mulitply
• dusent — is not dutzend (dozen), but tausend (thousand)
• Neugard — is the town name Naugard/Novograd; here more probably Novgorod
• gissen — mutmaßen, to estimate

An older source edition from 1866 had the Arabic numerals written as Roman numerals in a slightly odd notation variation: — for "17 werve hundert dusent" it had "XVII werve dusent"; — for "2800 dusent" it had "XVIII^C dusent"; and for "15 werve hundert dusent" it noted "XV werve dusent"

Which would translate a little freely into English as:

The king of Krakow had 17 times a hundred thousand people in his company, and King Witold of Lithuania had 2800 thousand people. The king of Novgorod and the Russians also joined them. They brought huge numbers of people from Russia to help them. In the same army was the Emperor of the Tartars, who had 15 times a thousand people, so that one could assume that all the people together numbered 50 times a hundred thousand and 100 times a thousand. The question now arises as to what he was to feed on the way. The answer is: what they found on the way: horses, donkeys, mules, oxen, sheep […]

Doing a little math spelled out: more than 5 million people from the side of Witold/Władysław II opposing the Teutonic order under Ulrich von Jungingen.

The crucial line spelling it out is:

viftich werve hundert dusent unde hundert werve dusent.

50 × 100.000 and 100 × 1000 = 5.100.000

No numerals involved at all, neither Roman nor Arabic.

The math in manuscript, editions and finally Wikipedia

The curious thing is that this one manuscript lists 1.5, 1.7 and 2.8 million participants. 2.8 being the Lithuanian contingent. This adds up to a round 6 million people involved from that side. The wikis deviate from that —unexplained— for the highest number and go for 'just' 2.7 million, and thus 5.9 million. That may be a late transmission error, but a rather small one in comparison.

However, the manuscript itself presents a total sum of participants on the side of the combined 'enemies of the Teutonic Order' as 5.1 million spelled out in words, not any numerals.
Sidenote: imagining just 28000 troops for the Lithuanians and leaving the other numbers as is as they are not disputable via envisioned 'footnoes/references' results in merely 3.2 million

This is a slight internal discrepancy in the original source manuscript between a calculated-by-reader-sum of 6 million, and the sum presented by the chronicler of 5.1 million is also left unexplained. However, we cannot just transform that one number given as "2800 thousand" into 28000 and arrive thusly at 3.228.000? Clearly 3.2 million is a worse match for 5.1 million compared to 6 million?

Transcripts & dictionaries used:

• Historische Commission bei der königlichen Akademie der Wissenschaften (eds): Die Chroniken der Deutschen Städte: T. 26. Bd. 2. Lübeck page 151. S.Hirzel: Leipzig, 1899. (Hirzel1866)
• Theodor Hirsch & Max Toeppen & Ernst Gottfried Wilhelm Strehlke & Walther Hubatsch [ed]: "Scriptores rerum Prussicarum. Die Geschichtsquellen der preußischen der preußischen Vorzeit bis zum Untergang der Ordensherrschaft (Vol. 1-6), (1861–1968), here: vol 3, Minerva: Leipzig, Frankfurt, 1866. (SRP1866, gBooks, p398–406, esp p404/5.)
• Faksimiles des Deutschen Rechtswörterbuchs (DRW): schiller-luebben v, Schiller-Lübben V S. 692-693

Relationship to other chronicles from Lübeck for that timeframe

This content is only found in one version of the original manuscripts of the "Croneke van Lubeke". These are:

Handschriften – Mss.

• Hamburg, Staats- und Universitätsbibliothek, Cod. hist. 33, f. 7r-37v saec. xv, Auszüge
• Hamburg, Staats- und Universitätsbibliothek, Cod. hist. 94, f. 1r-61r saec. xv, verstreute Auszüge
• Lübeck, Stadtbibliothek, Ms. Lub. 2° 1 heute in Jerewan/Armenien, saec. xiv ex.
• Lübeck, Stadtbibliothek, Ms. Lub. 2° 2 = zweiter Teil von Ms. Lub. 2° 1, saec. xv
• Lübeck, Stadtbibliothek, Ms. Lub. 2° 3 Abschrift saec. xvii aus Ms. Lub. 2° 1 und 2
• Lübeck, Stadtbibliothek, Ms. Lub. 2° 4

These are partly interwoven and overlapping, with sometimes unclear intertextual dependencies, some clearly following older versions of each other, but then deviating in unpredictable manners. Research hasn't reached a consensus explanation for these discrepancies.

The Ham. Cod. Hist. 33 is the only relevant manuscript here. It follows Ms. Lub. 2° 1/2 until 1276, then continues after that one ends in 1395 until 1413. It is speculated that this Ham.Cod.Hist.33 — which is the only source for the 'insane number' — was written in exactly 1413, by a somewhat sloppy writer with numerous other obvious errors in it. Readily apparent for a modern reader: Witold/Vytautas ruled the Grand Duchy of Lithuania, while a ruler he was strictly speaking not 'the King of Lettowe'.

The sources for the chronicle writer and their reliability

The editor of SPR1866 after inspecting the original manuscript himself in the Hamburg library says already explicitly:

A Lübeck Franciscan continuation of Detmar's chronicle is found in the manuscript of the latter at the Hamburg City Library no. 33 fol.; old no.636 (cf. Grautos 1,499 and II, Preliminary Report xvii ff.). It extends over the years 1400–1413 independently of other known continuations and, as far as 1408 ff. are concerned, was certainly not written until 1413.

Whether the manuscript, which admittedly belongs to the first half of the XVth century, offers the autograph of that continuator is doubtful because of some scribal errors. In the notes which Grautoff II, 582 ff. gives from this manuscript, precisely the most interesting of the passages relating to Prussia 1410 (cf. a.a.0.p.478–598) is intentionally omitted. For his description of the war events of this year in Prussia, the chronicler refers to the reports of two eyewitnesses who were also besieged in Marienburg, namely a rifleman and the Lector ["reading master"] of Culm, which is probably in the Franciscan monastery there. It is reasonable to assume that the latter came to Lübeck in 1413 at Whitsun (11 June) with the chapter of probably 400 Franciscans from the Order's province of Saxony (to which Culm also belonged; cf. 0. p. 17) mentioned in the sequel itself (Gr.II,601). Especially the savagery of the pagan hordes overrunning Prussia appears here in the strongly applied colours of mere rumour.

— SRP1866, editorial comment, p404.

Which reads in the original manuscript as, translated to English:

This I have described directly from the mouth of the people, who were in Prussia and on the Marienburg: a rifleman and another, who was a reading master [lector] at Culm, a truthful man, who saw and heard everything.

— SRP1866, p407–408.

Note: "rifleman" is translated from "bussenschůtte" (Büchse and 'shooter') but here, language-wise it is indistinguishable from 'crew of a bombard', for a weapon that was in use in that battle. Something like a culverin/Feldschlange or hand cannon/Handrohr —while now perhaps more associated to the word rifle— is less likely for the event. Although the curiously named for another castle of the same name near Darmstadt, _Tannenbergbüchse,_ is dated to 1399.

Which leaves us with two oral sources for the chronicle, giving a recognized by later editors embellished account, but with precise numbers written down in the original manuscript, transmitted accurately into the transcripts of the source editions.

Why the exaggerated numbers in the one source manuscript

However, the numbers for the total Polish-Lithuanian side from that one and only relevant manuscript are identical in all later transcripts and source editions: "50 × 100.000 + 100 × 1.000"

That all this is 'slightly' exaggerated — and in a familiar manner — is rather obvious from the preceding sentences. There, the chronicler elaborated when writing in 1413 in even more detail the composition of the opposing force:

'both kings, of Krakow and of Lithuania called in people from far away lands, unbelievers of 'countless numbers', among them Saracens, Turks, Tartars, infidels from Damascus, Persia, Medes, and Caspians (from where the red Jews live). So many the earth was shaking when the army moved.'

In short: many.

And 'a whole world of enemies' — if not simply 'the hordes from the East' — 'against the Teutons' is indeed the same theme tune played not only in 1410 but in 1914 again.

Thus the second battle of Tannenberg was seen as a late revenge of the Teutonic Order, even if one had to equate the Russians of 1914 with the Poles and Lithuanians of 1410. Sven Ekdahl rightly said: "The symbolism remained oblique".

— Udo Arnold: "Tannenberg (Grunwald) In der deutschen Tradition des 19. und 20. Jahrhunderts", Ordines Militares, Yearbook for the Study of the Military Orders, Vol 19, 2014, p241–253, doi. (Cf.: Sven Ekdahl: "Tannenberg/Grunwald—ein politisches Symbol in Deutschland und Polen", Journal of Baltic Studies, 22:4, 1991. p271–324, doi.)

From the beginning Teutonic and then Prussian historiography used this defeat in propaganda with a positive spin. Overwhelming forces, almost 'illegal' participation of heathens… This is visible for example already in the monument erected than printed transcriptions of the Lübeck chronicle:

1701, a large memorial stone was erected for the fallen Grand Master in the midst of the chapel ruins. In English translation, the German inscription reads:

“Here, in battle for German spirit and law, Grand Master Ulrich von Jungingen died a hero’s death on 15th July 1410”

— Ekdahl 2019

Honest error, deliberate exaggeration, or faulty transmission later on resulting in rumors being recorded: such exaggerations, of which the questioned chronicle sets the record, were indeed enormously useful:

In the propaganda of the Teutonic Knights after the defeat in 1410, the “pagan question” was the most important instrument for getting help from Central and Western Europe. Correspondence, chronicles, writings and Council records repeatedly point to the betrayal of Christianity by the use of non-Christian peoples in the armies of the Order’s opponents. Also, the Roman and Hungarian King Sigismund of Luxemburg highlighted this in his famous appeal of 20 August 1410 for help for the beleaguered Order.

— Sven Ekdahl: "Different points of view on the Battle of Grunwald/ Tannenberg 1410 from Poland and Germany and their roots in handwritten and printed traditions", Z Badań nad Książką i Księgozbiorami Historycznymi, Vol 13, 2019. doi

After elucidating the alleged source for this seemingly too big number from one German source, it seems prudent to highlight again that the Lübeck number, however absurd it may seem, is not the only unreliable source out there for this event: there are simply absolutely no reliable historical sources for the number of troops involved, not even on the exact places involved, and from neither side:

Reliable information on the size of troops there, are extremely controversial figures in the literature. German studies most often report 12,000 to 15,000 soldiers from the Order and 20,000 to 25,000 from the enemy. Polish and Lithuanian historians give much higher numbers. Without dwelling on this issue in more detail, I would, however, like to point out in this connection that Gerard Labuda recently referred to a source from the 1930s, which refers to 30,000 men in the Lithuanian army. Important are two letters from the Comtur Commander of Ragnit to the Marshal of the Order and the Commander of Brandenburg dated 13 June 1410, which show that each land of Samogitia supplied 400 hors*m*n and that three hors*m*n had one wagon; Anthony Prahaska in Codex epistolaris Vitoldi mistakenly calls this number instead of 300. Just as it is untrue information, the alleged soldiers of the Order made in the campaign against Prussia, with 60,000 horses: According to the sources […] it is only about 2000 horses. Such explanations or variations do not contribute to clarifying the debatable question about the numbers and the numerical composition of the troops.

— Sven Ekdahl: "Бітва пад Танэнбергам і яе значэнне ў гісторыі ордэнскай дзяржавы" (The Battle of Tannenberg and its significance in the history of the Order's state), "Бітва пад Танэнбергам і яе значэнне ў гісторыі ордэнскай дзяржавы", Беларускі Гістарычны Агляд (Belarusian Historical Review), Vol 2, No1–2, 2020.

What we have to rely on are mostly modern reconstructions and approximations for the true number of participants in that battle.

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On the proper paleography for medieval Roman numerals and fantastically wrong 'theories' appreciated by HistorySE users who like attacking in bolded comments

Considering the allegations below in comments that the above source edition, which is transcribed rather faithfully from what is visible on the printed page, with Arabic numerals clearly spelling out "2800", which according to that theory should have been a transcription error from one source edition to another source edition: that is rather unlikely. And we will see why it is an utterly false personal theory on every level.

Before the internet, historians engaged in source editions were usually of a quite obsessive character, often fiercly insisting on not copy-pasting old info down the river, but going ad fontes as far as possible. Meaning they would usually insist on examining the very source material themselves, that is reading the manuscripts αὐτοψία. The editor of SRP1866 explicitly emphasizes that he himself examined the only one relevant and embellished manuscript from Hamburg Library.

The theory that another source edition would be the reason for a transcription error in copying it is further weakened when looking closely at the very page in the Scriptores Rerum Prussicarum (SRP) Vol 3, p405. There it indeed says "XXVIII^C":

That is not any capital 'G', and the 'theory'fantasy that this would be a footnote-like superscript 'G' (in the middle of a numeral?) also suffers from the problem that there just is no corresponding footnote on that page for G. On that page we have footnotes for a–f (lower case, no upper case anywhere), plus Arabic numeral footnotes 1–3.

The lower part of the page, with all footnotes there are, from a–f, but no 'G':

Rather surprisingly, even the Google-OCR renders the result of that numeral almost quite correctly as "XXVIIIC".

Whole page in context:

The same transcript repeats this style one page after that on p406:

Desser en deel dusent oder twedusent makeden sik in dat heere unde sloghen in enen orden den vienden aff IIII^C eder V^C.

Clearly meaning '400' or '500'.

Same page again:

Ere sette begunden sik mit ertbevinghe, also dat beschreven is in der króneken in den jare Christi M°CCII° unde XLII, XLIII, XLV, XLVI, LVI, LVIII°, LX°, LXI°, dar vele wunders steyt van en bescreven van erer greselichkeit

It is true that this does not conform to 'the' 'standard model' of Roman numeral construction, but the variations that were used are, well, numerous. Sometimes even a just sloppy handwriting needs representation in a source edition… But here we see simply an older custom that fell into disuse.

Similarly, hundreds can be written with the number of hundreds followed by the hundreds marker as a superscript: thus 300 is written III^c

— FrenchWP

A variant of this spelling uses superscripts for better readability and clarity. An example is the year 1519 written as XV^CXIX as in German "fünfzehnhundertneunzehn" or in French quinze-cent-dix-neuf. In some French texts from the 15th century and later, one finds constructions such as IIII^XXXIX for 99, reflecting the French reading of this number as quatre-vingt-dix-neuf (four-sixty and nineteen). Similarly, in some English documents one finds e.g. 77 written as "iii^xxxvii" (which could be read "three-score and seventeen").

— GermanWP

If you need still more convincing:

— Charles Burnett: "The Palaeography of Numerals", pp25–38, in: Frank T. Coulson & Robert G. Babc**k (eds): "Oxford Handbook of Latin Paleography", Oxford university Press: Oxford, New York, 2020, p30: "MS Avignon, Bibliothèque municipale, 1086, fol. 68r: M°CCCC43°".
Or more explicitly
— John Newsome Crossley: "Old-fashioned versus Newfangled: Reading and Writing Numbers, 1200–1500", Studies in Medieval and Renaissance History, Third Series, Volume 10, 2013, pp.79–109.)

And this

7.6 The well-known rule that a numeral standing to the left of a larger roman numeral is to be subtracted from it (e.g. ↀIↃↃ = 4000) appears to have been little honored by the ancient Romans themselves, and there are only rare examples from the Middle Ages.

[…]

7.73 The numeral letters C and M, especially in the later Middle Ages, were frequently written as superscripts to smaller numbers as a sign of multiplication: VIII^c = 800; XI^c = 1100; II^m = 2000.

— Adriano Cappelli: "The elements of abbreviation in medieval Latin paleography", University of Kansas: Lawrence, 1982. (pdf)

Just consider on the very same page of SRP1866 we see one year-date rendered as "M°CCCC°X°" (or superscript 0, can't decide what looks better here):

Since that is rendered in the Hirzel1899 edition as Arabic numeral "1410", and is also neither a footnote for "0" (three 'same number' footnotes within one number?), nor standard school Roman numeral construction either, I conclude that both editions, SRP1866 and Hirzel1899 were transcribing directly from the 'continuation of Detmar's Cronike von Lubeke' as found in Ms Ham Cod Hist 33, both reading the correct number as meant by the scribe — the correct number as corresponding roughly calculated for the sum total given, and just used different representations on page for what is an unusual looking Roman numeral in the manuscript.

Normatively prescriptive 'theories' — like in upvoted comments below here or in other answers — with present day rules transposed to the past to pass judgements – aren't always adequate. They are anachronistic and do not fit the bill here.

We see the total tally being quite unequivocally spelled out in all clarity, as well in that medieval manuscript source, as accurately transcribed into modern source editions, repeat: accurately, more than once.

Fancy 'theories' that a very late 19th century scribal error would have only crept in by lazy modern source editors copying each other are clearly completely bogus.

This one medieval scribe just did what other scribes at the time did as well: conforming to their rules and practices, not present day 'orderly' rules and prescriptions.

The unbelievable high numbers come directly from the Lübeck source, one manuscript of said chronicle, where they were recorded after the fact in 1413, with embellishment from hearsay or rumours.

The crucial number in the inquired chronicle manuscript MS Ham Cod.hist.33 174r/175v 'Detmar' as pictures

The Lübeck chronicle snippet in question just does use the fancy superscript c and Detmar's disciple just means 2800 thousands:

xxviij^c̣ (duze ͡t)

= 28-^hundred thousand

This number 'fits' the 'total' given just a few lines later, with 5.1 million:

If instead you'd reduce this number artificially and counterfactually — to accommodate a fancy theory — down to 28000 (because you imagine to see a footnote 'G' within the numeral where a 'g' should be used for footnote marks, and no corresponding footnote 'G' or 'g' exists on that page, but in reality a clearly recognizable superscript C is found in a late edition, matching perfectly the 608 year old parchment manuscript) the written out number suddenly is widely off. This 'personal theory' is disproven as false in every version of the sources: original and transcripts.

If anyone still thinks this would be a 19th century footnote mark in a 1413 manuscript — that never uses any footnotes at all — because modern day school rules would say the scribe that did this was simply a fool for not knowing how HistorySE users expect Roman numerals to be formatted 'correctly', we're done here in more than one way…

The manuscript this question asks for whether it exists: it is one single document from Lübeck, integrated in the tradition of other chronicles from that time, but isolated in being the only one describing this specific event at Grunwald, with truly immensely unrealistic numbers, from hearsay three years later.

But it spells it out with words in exactly this way: five million and one hundred thousand.

It is easily justifiable to say 'there is that source that claims 5.1 million', and it remains difficult to justify 'and that's the real number, one source says so.'