I think real simply if you go to Jesus and find out what he said about the first five books you'll be amazed that he stands over the liberal theologians as knowing who was the author of the Pentateuch.
Matt 8:4 And Jesus saith unto him, See thou tell no man; but go thy way, shew thyself to the priest, and offer the gift that Moses commanded, for a testimony unto them.
Matt. 19:7 They say unto him, Why did Moses then command to give a writing of divorcement, and to put her away?
Matt 22:24. Saying, Master, Moses said, If a man die, having no children, his brother shall marry his wife, and raise up seed unto his brother.
Mark 7:10 For Moses said, Honour thy father and thy mother; and, Whoso curseth father or mother, let him die the death:
Mark 10:3 And he answered and said unto them, What did Moses command you?
Mark 10:4
And they said, Moses suffered to write a bill of divorcement, and to put [her] away.
Mark 12:26 And as touching the dead, that they rise: have ye not read in the book of Moses, how in the bush God spake unto him, saying, I [am] the God of Abraham, and the God of Isaac, and the God of Jacob?
Luke 16:32 And he said unto him, If they hear not Moses and the prophets, neither will they be persuaded, though one rose from the dead.
Luke 24:27 And beginning at Moses and all the prophets, he expounded unto them in all the scriptures the things concerning himself.
Luke 24:44 And he said unto them, These [are] the words which I spake unto you, while I was yet with you, that all things must be fulfilled, which were written in the law of Moses, and [in] the prophets, and [in] the psalms, concerning me.
John 1:17 For the law was given by Moses, [but] grace and truth came by Jesus Christ.
John 7:19 Did not Moses give you the law, and [yet] none of you keepeth the law? Why go ye about to kill me?
John 8:5 Now Moses in the law commanded us, that such should be stoned: but what sayest thou?
I think the authorship was clearly spoken by the greatest theologian, our God and Saviour Jesus Christ.