No, He did not bear false witness! His witness was “not true” (v.31) if He was the only witness of Himself (Deut. 19:15). But He had another witness (v.32), and this witness cannot be a mere man, for His witness “is true” all by itself. John speaks here of the Father, who bore witness of Him at His baptism (Mt. 3:17).
After His Father, the Lord next called John the Baptist to the witness stand (John 5:33). The Jews “sent” to John in John 1:19, and he bore witness to the Lord (v.20-29). So now the Lord’s witness count is up to three, fulfilling the fullest extent of the Law (Deut. 19:15).
Before calling His next witness, the Lord adds a puzzling comment about John’s testimony (John 5:34). Why would He not receive testimony from man? Because “all men are liars” (Ps.116:11). But if John was the greatest man ever born (Mt.11:11), why wouldn’t the Lord receive his testimony? Because the best of men are only men at best, and so the testimony of the best of men is the testimony of men at best. Even the best of men had his doubts (Mt.11:2,3), so how much was his testimony really worth?
If the Lord didn’t receive John’s testimony, why did He bring it up? He knew they received the testimony of men, so He brought it up, as He told them, “that ye might be saved” (John 5:34). The Lord wanted even these enemies who wanted to kill Him to be saved (5:18 cf. Rom. 5:18).
Now why would the Lord call John “a shining light” (5:35)? A man’s good works are his light (Mt.5:16), and being the best of men he did more good works than any man. Notice Matthew 5:16 doesn’t say to let your light shine so men see your light. It says let your light shine so men see your good works, defining light as good works. Of course, John’s light was not a burning light like the sun but rather a reflective light like the moon, reflecting the light of the Lord (John 1:9). So why does the Lord call him a “burning” light (Jo.5:35)? You’ve never had a moonburn, but John’s good works burned that hot! Do yours?
The Lord’s enemies (John 5:18) “were willing for a season to rejoice in his light” (v.35). The fact that they came initially to his baptism proves this (Mt.3:1-7). John preached repentance, and men know by nature they need to repent. Of course, the Pharisees didn’t think they had that much of which to repent, and so stopped rejoicing in John when he called them a generation of vipers!
When the Lord announced that His next witness would be “greater” (John 5:36), what witness could be greater than that of the greatest man ever born of women? “The works” or miracles He did, especially the kind of miracles He did. When He said “Peace, be still” to the storm (Mark 4:35-41), for instance. Also, after the Lord walked on water (Jo.6:15-21), “immediately the ship was at the land whither they went.” Compare this to how the God of the Old Testament could still storms and bring ships safely to land (Ps.107:23-29)! When the Lord did these things, men should’ve known He was the God of the Old Testament!
But how could the Lord say that the Jews had not heard the Father’s voice “nor seen His shape” (John 5:37)? Hadn’t they heard the Father at His baptism, and seen the Spirit descend on Him “in a bodily shape” (Luke 3:21,22)? Well, there is more than one way to hear God’s voice. In Psalm 95:6-8, the psalmist says “To day, if ye will hear His voice…”, but God hadn’t spoken to Israel since they begged Him not to (Ex.20:19). The psalmist was begging them to hear His voice in the Scriptures.
And so the Lord is saying that while the Jews had studied the Scriptures, they had never heard His voice in the Scriptures, nor seen the shape of Himself that He was trying to portray to them in the Scriptures. That’s why they didn’t recognize the Lord’s voice nor His shape when He appeared to them. Since the Lord had already talked about how the Father had borne witness to Him at His baptism (John 5:32), in Verse 37 He is referring to the witness the Father bore to Him in Scripture! That’s the context. They couldn’t hear the Father’s voice or see His shape in Scripture because, as the Lord told them, “ye have not His word abiding in you” (v.38).