Was it and is it a common Christian belief to say that the 5 books of the Torah were written by Moses?

Upvote:0

Yes is the answer to the OP. To add about church fathers, here is Clement of Rome's First Epistle to the Corinthians.

Chapter XLIII.—Moses of old stilled the contention which arose concerning the priestly dignity. And what wonder is it if those in Christ who were entrusted with such a duty by God, appointed those [ministers] before mentioned, when the blessed Moses also, “a faithful servant in all his house,”186 noted down in the sacred books all the injunctions which were given him, and when the other prophets also followed him, bearing witness with one consent to the ordinances which he had appointed? For, when rivalry arose concerning the priesthood, and the tribes were contending among themselves as to which of them should be adorned with that glorious title, he commanded the twelve princes of the tribes to bring him their rods, each one being inscribed with the name187 of the tribe. And he took them and bound them [together], and sealed them with the rings of the princes of the tribes, and laid them up in the tabernacle of witness on the table of God. And having shut the doors of the tabernacle, he sealed the keys, as he had done the rods, and said to them, Men and brethren, the tribe whose rod shall blossom has God chosen to fulfil the office of the priesthood, and to minister unto Him. And when the morning was come, he assembled all Israel, six hundred thousand men, and showed the seals to the princes of the tribes, and opened the tabernacle of witness, and brought forth the rods. And the rod of Aaron was found not only to have blossomed, but to bear fruit upon it.188 What think ye, beloved? Did not Moses know beforehand that this would happen? Undoubtedly he knew; but he acted thus, that there might be no sedition in Israel, and that 17 the name of the true and only God might be glorified; to whom be glory for ever and ever. Amen. -source-

Here is Augustine with the same belief that Moses wrote the first five books.

I would hear and understand, how “In the Beginning Thou madest the heaven and earth.” Moses wrote this, wrote and departed, passed hence from Thee to Thee; nor is he now before me. -Confessions-

And here is Justin Martyr.

I will begin, then, with our first prophet and lawgiver, Moses; first explaining the times in which he lived, on authorities which among you are worthy of all credit. For I do not propose to prove these things only from our own divine histories, which as yet you are unwilling to credit on account of the inveterate error of your forefathers, but also from your own histories, and such, too, as have no reference to our worship, that you may know that, of all your teachers, whether sages, poets, historians, philosophers, or lawgivers, by far the oldest, as the Greek histories show us, was Moses, who was our first religious teacher. -source-

Some 1,500 years later, Matthew Henry will write the same.

We have before us that part of the Old Testament which we call the Pentateuch, or five books of Moses, that servant of the Lord who excelled all the other prophets, and typified the great prophet. -source-