Albert Barnes on John 5:34

I receive not testimony from men. I do not depend for proof of my Messiahship on the testimony of men, nor do I pride myself on the commendations or flattery of men.

But these thing, &c. "This testimony of John I adduce that you might be convinced. It was evidence of your own seeking. It was clear, full, explicit. You sent to make inquiry, and he gave you a candid and satisfactory answer. Had you believed that, you would have believed in the Messiah and been saved."

Men are often dissatisfied with the very evidence of the truth of religion which they sought, and on which they professed themselves willing to rely.

(g) "but these things" Jn 20:31, Rom 3:3