Chapter five begins with Christ healing a man who had been paralyzed for 38 years. The man lay by a pool—the waters of which were stirred by an angel for healing (5:2-4)—until Jesus asked Him, "Do you want to be made well" (5:6)? The man was healed after Jesus commanded him to take his bed and walk (5:8). St. John Chrysostom teaches that this episode foreshadows Holy Baptism: "This miracle was done so that those (at the pool by the Sheep's Gate) who had learned over and over for such a long time how it is possible to heal the diseases of the body by water might more easily believe that water can also heal the diseases of the soul."
Instead of rejoicing in this miraculous healing, some of the people objected because it occurred on the Sabbath (when it was unlawful to engage in any work) (5:8, 16). This leads into the remainder of the chapter, in which Jesus explained His authority for engaging in such work: He said both He and His Father had been working (Blessed Theophylact says the continual functioning of nature demonstrates God?s providential work (for example, see Acts 17:28)), thereby stating that He was equal with God (5:18). He even added that He does the things the Father has shown Him (5:19-20), which according to St. Cyril of Alexandria means "the Father depicts Himself wholly in the nature of His Son and shows in His Son His own natural properties in order that from these properties He has and shows, the Son may know what and Who His Father is that begat Him by nature."
This is quite a claim—so where is the evidence? Jesus went on to describe two works done by His Father that He also could do. First, both the Father and Son can raise the dead (5:21, 25); the Church Fathers stress the fact that Christ can give life "to whom He will" (5:21), because this demonstrates the fullness of Christ's divine nature and His authority. Second, the Father has given His Son the authority to judge (5:22, 27). St. Hilary of Poitiers directly relates this to the first work: "All judgment has been given to Him since He gives life to whomever He will." This means we should worship the Son as we do the Father (5:23)—St. Cyril of Alexandria describes it as "crown(ing) both with equal honor." Whether we accept or reject Christ—and how we live our lives in accordance with this decision—will ultimately determine whether we spend eternity with God or apart from Him (5:29).
Jesus said all of this about Himself, but are there any other witnesses to His divinity and authority? The testimony of only one person is often untrue—Christ anticipated that some might even have said this about His self-testimony (5:31). Jesus therefore presented several additional witnesses: St. John the Forerunner (5:33-35); Christ?s works (5:36); God the Father (5:37); Holy Scripture (5:39); and the Holy Prophet and God-seer Moses (5:45-47). Unfortunately, rather than listening to these witnesses and giving Christ honor, the people instead focused only their own honors (5:44); in fact, Christ predicted that the people would give more honor to the Antichrist than to the real Messiah (5:43).