In John 5:31ff, Jesus mentions six witnesses that testify on His behalf that He was in fact sent by God the Father and was seeking to accomplish His will in all things.
WITNESS #1: JESUS HIMSELF
Our Lord began by noting that if He alone testified on His own behalf that such testimony would not be deemed valid. Two witnesses are better than one (cf. Deut. 17:6). However, Jesus will supply many witnesses--besides Himself--to substantiate His case as the Christ, the Son of God (e.g., John 5:32 - "there is another who bears witness of Me").
The language used in 5:32 seems to refer to God the Father. There is a sense in which all of the witnesses mentioned in the following verses are really testimonies of Christ through the Father. The Father will be explicitly named as a witness in 5:37.
WITNESS #2: JOHN THE BAPTIZER
The Father testified of Christ through John the baptizer (5:33). John's ministry attested to the fact that Jesus was the Lamb of God, the Savior of the world (1:29-34).
Jesus affirmed in 5:34 that He did not accept mere human testimony. Of course, John's testimony was not such since it was inspired of God. Jesus mentioned John's testimony in the hope that the Jews might accept John's assessment of Him and be saved. After all, at one time, many of them "were willing to rejoice in [John's] light" (5:35). Would they be willing to do so now by accepting John's testimony of Christ?
WITNESS #3: JESUS' WORKS
The Father, through Jesus' own works, testified of His Son in a stronger way than John ever did. Jesus' "works" should not be confined to His miracles in this context. The works Jesus did also included His life of perfect holiness, the prophecies He fulfilled, and the accomplishment of man's redemption. All of these things prove Him to be the Son of God.
We will continue this study tomorrow.