In verses 33-35, Jesus is really bearing witness to John, who had borne witness to the truth as a burning and a shining lamp. John's witness was marked by both warmth and light, yet he was only a "lamp"-- that is the word the Lord used-- whilst Jesus was the true light, like the sun shining in its strength.

Now the sun needs no witness from a mere lamp, even though it burns and shines. The works which the Father had given Jesus to finish were like beams of light thrown off by the sun. They were a greater witness to Him than anything that John could say. They were so obviously divine that they proved Him to be the Sent One of the Father (John 5:36).

And then, in the third place, the Father Himself had borne witness to Him-- notably, at the time of John's baptism (John 1:32-34)-- but they, being utterly carnal, had not appreciation of it (John 5:37-38). They wanted something which would appeal to their natural powers of siight or hearing. They knew nothing of that word of the Father which brings spiritual illumination.

Lastly, there were the holy Writings (John 5:39). These did indeed testify of Him, and they searched them. They thought they had eternal life in the Scriptures, but Christ is the Giver of it, and to Him they would not come.

If by searching the Scriptures men are conducted to Christ, then indeed they have eternal life through the Scriptures. Otherwise they merely gain knowledge of a technical, theological sort and yet remain in spiritual death. These words are most illuminating as to what the true function of Scripture is.