What is the context for Napoleon's quote "[the Austrians] did not know the value of five minutes"?

The context for this disputable attribution and disputable accuracy quote is the Battle of Rivoli.

The battle of Rivoli (14 January 1797) was the most comprehensive of Napoleon's victories in Italy during his campaign of 1796–97. At the end of the pursuit that followed the victory the French had captured more than half of an Austrian army of 28,000, despite being significantly outnumbered at the start of the campaign.

And here supposedly from the horse's mouth:

'Arriving about two in the morning (by another of his almost incredible forced marches) on the heights of Rivoli, he, the moonlight being clear, could distinguish five separate encampments, with innumerable watch-fires, in the valley below. His lieutenant, confounded by the display of this gigantic force, was in the very act of abandoning the position. Napoleon instantly checked this movement; and bringing up more battalions, forced the Croats from an eminence which they had already seized on the first symptoms of the French retreat.

Napoleon's keen eye, surveying the position of the five encampments below, penetrated the secret of Alvinzi ; namely, that his artillery had not yet arrived, otherwise he would not have occupied ground so distant from the object of attack. He concluded that the Austrian did not mean to make his grand assault very early in the morning, and resolved to force him to anticipate that movement. For this purpose, he took all possible pains to conceal his own arrival ; and prolonged, by a series of petty-manoeuvres, the enemy's belief that he had to do with a mere outpost of the French. Alvinzi swallowed the deceit ; and, instead of advancing on some great and well-arranged system, suffered his several columns to endeavour to force the heights by insulated movements, which the real strength of Napoleon easily enabled him to baffle. It is true that at one moment the bravery of the Germans had nearly overthrown the French on a point of preeminent importance ; but Napoleon himself galloping to the spot, roused by his voice and action the division of Massena, who, having marched all night, had lain down to rest in the extreme of weariness, and seconded by them and their gallant general,* swept every-thing before him. The French was in : the Austrian's artillery position (according to Napoleon's shrewd guess) had not yet come up, and this circumstance decided the fortune of the day. The cannonade from the heights, backed by successive charges of horse and foot, rendered every attempt to storm the summit abortive ; and the main body of the Imperialists was already in confusion, and, indeed, in flight, before orte of their divisions, which had been sent round to outflank Bonaparte, and take higher ground in his rear, was able to execute its errand. When, accordingly, this division (that of Lusignan) at length achieved its destined object it did so, not to complete the miserj' of a routed, but to swell the prey of a victorious enemy. Instead of cutting off the retreat of Joubert, Lusignan found himself insulated from Alvinzi, and forced to lay down his arms to Bonaparte.

"Here was a good plan", said Napoleon, "but these Austrians are not apt to calculate the value of minutes."

Had Lusignan gained the rear of the French an hour earlier, while the contest was still hot in front of the heights of Rivoli, he might have made the 14th of Januarj- one of the darkest,

–– Louis Antoine Fauvelet de Bourrienne: "Memoirs of Napoleon Bonaparte", Hutchinson: London, 1904, p44. (archive org) From The French Of F. De Bourrienne
Private Secretary to Napoleon, and Minister of State under the Directory , the Consulate, the Empire and the Restoration.

When the Memoirs first appeared in 1829 they made a great sensation. Till then in most writings Napoleon had been treated as either a demon or as a demi-god. The real facts of the case were not suited to the tastes of either his enemies or his admirers.
_{–– Ramsay Weston Phipps, traslator, from he preface of the 1885 edition at Charles Scribner's Sons, said to be the best English translation}

A big caveat is found in:

The Memoirs His book gives a vivid, intimate, detailed account of his interactions with Napoleon and his mother, brothers and sisters; with his first wife Joséphine de Beauharnais and her children; with notable French politicians; and with the marshals, he was especially friendly with Jean Baptiste Jules Bernadotte the future King of Sweden when they both were in Northern Germany. His narrative is invigorated by many dialogues, not only of those in which he was a speaker but even of conversations that he only was told about by others. Their exactitude may be suspect but surely they give a memorable portrait of his times. Many judgments are supported by quotes from his stockpile of documents. Naturally his narration is colored by his complicated relationship with his subject: close friendship, working together intimately for years, followed by dismissal and humiliating rejection. He tries to be balanced and gives many examples of Napoleon’s brilliance, his skill at governance, and his deft political maneuvers, while deploring his inexorable grabs for personal and familial power and wealth, his willingness to sacrifice French lives, and his abhorrence of a free press. Military campaigns are left for professional judges. One of his bombshells is the claim that the Grand Army based at Boulogne was never meant to invade England, too chancy an enterprise: it was a diversion to keep British forces at home. Of course the book infuriated devoted Bonapartists; two volumes of criticisms were published promptly to attack his credibility. Controversy was still raging half a century later. His book is not a source in which to check particular facts, but as Goethe wrote: “All of the nimbus, all of the illusions, with which journalists and historians have surrounded Napoleon, vanishes before the awe-inspiring realisms of this book…”.

Karl Marx knows this to report:

His financial difficulties forced him to seek refuge in Belgium in 1828 on a country estate of the Duchess of Brancas in Fontaine l'Evêque, not far from Charleroy. Here he wrote his "Memoirs" (10 volumes, Octav), supported by Mr de Villemarest and others, which appeared in Paris in 1829 and caused great excitement. He died in an asylum (Irrenhaus).
_{–– Karl Marx/Friedrich Engels - Werke, (Karl) Dietz Verlag, Berlin. Band 14, 4. Auflage 1972, unveränderter Nachdruck der 1. Auflage 1961, Berlin/DDR. S. 115-116.}

In fact, not only is the accuracy of that quote a bit transformed compared to the added detail in the phrasing as presented in the question and the form 'good quote seekers' or managers are familiar with. It is in doubt at the root. A more thorough assessment gives the source of that quote quite a different meaning:

Distance from the lived event is one reason that veterans often wrote about what they believed to be the “truth” in history and spoke of accurate representations of the past. Historians cannot. They generally consider memoirs from this period inaccurate and often discount them as unreliable. On the face of it, this assessment seems reasonable. We know that memories can be falsified and that veterans can end up recounting events in which they never took part, repeating stories that they heard elsewhere and that they incorporate as their own.

Indeed, contemporaries were perfectly aware of the tricks that time and memory could play on the individual attempting to recount events taking place many years earlier.^*

If, however, these memoirs are regarded as “linguistic documents” that contain “culturally developed ideologies,” the accuracy or inaccuracy of a particular memoir or a specific event recounted is less important than the values transmitted in these testimonies, such as national glory and military valor, and is also less important than that the narrative, even if fictionalized, rings true, especially to the nineteenth-century reader. If this then offers a new reading of memoirs, not as historical documents in any traditional sense but as sources of information about how the past was recalled and recollected.
^{– * Louis-Antoine Fauvelet de Bourrienne, Mémoires de M. de Bourrienne, ministre d’Etat, sur Napoléon, le Directoire, le Consulat, L’Empire et la Restauration, 10 vols. (Paris, 1829), 1:8; Léon-Michel routier, Récits d’un soldat: De la République et de l’Empire (Paris, 2004), 17.}
_{–– Philip G. Dwyer: "Public Remembering, Private Reminiscing: French Military Memoirs and the Revolutionary and Napoleonic Wars", French Historical Studies (2010) 33 (2): 231–258. DOI}

Now the corrupted version displayed in the question

The reason I beat the Austrians is, they did not know the value of five minutes. –– Napoleon.

Seems to be a later version. The context for that is 'inspirational quote alteration', like on the internet when you see no proper source attribution attached. That is found in: S. Pollock Linn: "Golden gleams of thought, from the words of leading orators, divines, philosophers, statesmen and poets", Chicago: McClurg, 1891. (p25 on archive.org).

_{In that context:
All animals are equal, but some animals are more equal than others. –– Dolly (sheep)}

Marden is possibly cribbing from chapter 7 of John Gibson Lockhart's The history of Napoleon Buonaparte which seems to have been published in 1829 and reissued many times since. Lockhart wrote about the 14 January 1797 Battle of Rivoli:

"Here was a good plan," said Napoleon, "but these Austrians are not apt to calculate the value of minutes."

I do not know what Lockhart's source was. I assume Napoleon did say (or write) something of the sort: Lockhart does not seem -- to me -- to be a fabricator.

In his book Pushing to the Front (1894), Orison Swett Marden wrote:

Napoleon laid great stress upon that ‘supreme moment,’ that ‘nick of time’ which occurs in every battle, to take advantage of which means victory, and to lose in hesitation means disaster. He said that he beat the Austrians because they did not know the value of five minutes; and it has been said that among the trifles that conspired to defeat him at Waterloo, the loss of a few moments by himself and Grouchy on the fatal morning was the most significant. Blücher was on time, and Grouchy was late. It was enough to send Napoleon to St. Helena, and to change the destiny of millions.