John Chrysostom — as excerpted in the Catena Aurea on John 5:31-40

“(Hom. xl. 3) Or the connection may be given thus. They might say to Him, How, if we have never heard God’s voice, has God borne witness to you? So He says, Search the Scriptures; meaning that God had borne witness of Him by the Scriptures. He had borne witness indeed at the Jordan, and on the mount. But they did not hear the voice on the mount, and did not attend to it at the Jordan. Wherefore He sends them to the Scriptures, when they would also find the Father’s testimony. (Hom. xli. 1). He did not send them however to the Scriptures simply to read them, but to examine them attentively, because Scripture ever threw a shade over its own meaning, and did not display it on the surface. The treasure was, as it were, hidden from their eye. He does not say, For in them ye have eternal life, but, For in them ye think ye have eternal life; meaning that they did not reap much fruit from the Scriptures, thinking, as they did, that they should be saved by the mere reading of them, without faith. For which reason He adds, Ye will not come to Me; i. e. ye will not believe on Me.”