31 If I bear witness of myself, my witness is not true. 32 There is another that beareth witness of me; and I know that the witness which he witnesseth of me is true. 33 Ye sent unto John, and he bare witness unto the truth. 34 But I receive not testimony from man: but these things I say, that ye might be saved. 35 He was a burning and a shining light: and ye were willing for a season to rejoice in his light. 36 But I have greater witness than that of John: for the works which the Father hath given me to finish, the same works that I do, bear witness of me, that the Father hath sent me. 37 And the Father himself, which hath sent me, hath borne witness of me. Ye have neither heard his voice at any time, nor seen his shape. 38 And ye have not his word abiding in you: for whom he hath sent, him ye believe not. 39 Search the scriptures; for in them ye think ye have eternal life: and they are they which testify of me. 40 And ye will not come to me, that ye might have life. 41 I receive not honour from men. 42 But I know you, that ye have not the love of God in you. 43 I am come in my Father’s name, and ye receive me not: if another shall come in his own name, him ye will receive. 44 How can ye believe, which receive honour one of another, and seek not the honour that cometh from God only? 45 Do not think that I will accuse you to the Father: there is one that accuseth you, even Moses, in whom ye trust. 46 For had ye believed Moses, ye would have believed me: for he wrote of me. 47 But if ye believe not his writings, how shall ye believe my words" (John 5:31-47)

Jesus does not need testimony from John the Baptist to prove Who He is. He mentions the testimony of John so that the hearers might be saved.

But what does Jesus mean by saved? Saved from what?

First of all, we can see from the context that Jesus is NOT referring to the eternal salvation of the doubting Pharisees. I have left the verse numbers in the quote above for more easy reference. Verse 38 says that the word of God does not abide in these men. Verse 40 says that these men will NOT come to Jesus for life. This is the same as chapter 6 when Jesus says that all the Father givehe me shall come to me. In that context we can see Jesus ultimately defines "come" as the resurrection of eternal life. Finally, verse 42 seals the identity of these men. Jesus says He knows them and therir true nature. The love of God is not in them and therefore they do not love God or His Son. 

Clearly, the salvation under consideration in verse 34 CANNOT be eternal.

John’s testimony was much like the testimony of other prophets who God sent to warn the nation of Israel against a national calamity that would come if Israel did not repent. He asked the Pharisees, "who hath warned thee to flee the wrath to come?" Peter and Paul both mention the prophecy of Joel in their teachings. Joel's warning concerned a captivity by the Chaldeans or the Babylonians if Israel did not repent. Peter and Paul use this same argument regarding the destruction that would come upon Israel at the hands of the Romans.

Notice also the word of Jesus in reference to this warning:

"When ye therefore shall see the abomination of desolation, spoken of by Daniel the prophet, stand in the holy place, (whoso readeth, let him understand:) let him which is on the housetop not come down to take any thing out of his house: neither let him which is in the field return back to take his clothes. And woe unto them that are with child, and to them that give suck in those days! But pray ye that your flight be not in the winter, neither on the sabbath day: for then shall be great tribulation, such as was not since the beginning of the world to this time, no, nor ever shall be. And except those days should be shortened, there should no flesh be saved: but for the elect’s sake those days shall be shortened."(Matthew 24:15-22)

While other positions of Jesus' discourse in Matthew 24-25 may point to the end of the world, this portion clearly speaks about a national calamity that will occur IN TIME. If the end of the world is coming, there would be not need to "flee." No, Jesus is clearly referring to the destruction of Jeruslaem that would occur in 70 AD.

Here in John 5, Jesus is warning against this same national judgement. Those that believed Jesus was the Son of God would believe His words. They would also believe His warnings as well those of the Apostles. This belief would lead them to flee from Jerusalem before the armies of Titus would take siege. Therefore, they would be SAVED from that wrath.