Jesus points to John the Baptist’s testimony, the works he does, the Father’s testimony, and the Scriptures (John 5:33–39). He also says Moses’s writings accuse those who reject him (John 5:45–47).
In John 5:31–40 Jesus lays out a chain of witnesses that point beyond self-praise. He names John the Baptist’s testimony, but then points to something greater: the works he is doing and the Father who sent him. He turns the focus onto his listeners, saying they have not truly taken in the Father’s word, even though they study Scripture. This section continues Jesus’ response after controversy over healing on the Sabbath and the claim that his actions match the Father’s work (earlier in John 5). The argument now shifts from what Jesus says about his role to how that claim is supported.
Jesus frames his identity claim in terms of a chain of testimony rather than self-praise. His point is not that he has nothing to say about himself, but that self-testimony by itself does not establish the kind of credible witness his audience expects (verse 31).
A careful answer keeps the immediate passage, the book's argument, and the whole-Bible storyline together, so the question is answered in context instead of as a detached idea.
Start with John 5:33-39, then read the surrounding section so the answer stays connected to the passage's flow.
33You have sent to John, and he has testified to the truth.
34But the testimony which I receive is not from man. However, I say these things that you may be saved.
35He was the lamp that burns and shines, and you were willing to rejoice for a while in his light.
36But the testimony which I have is greater than that of John, for the works which the Father has given me to accomplish, the very works that I do, testify about me, that the Father has sent me.
37The Father himself, who sent me, has testified about me. You have neither heard his voice at any time, nor seen his form.
38You don`t have his word living in you; for whom he sent, him you don`t believe.
39You search the scriptures, because you think that in them you have eternal life; and these are they which testify about me.