A few considerations:
This text can't be about faith or belief. The sick man was just laying there and did not know who it was that healed him (5:13). He did not believe in Christ and I suppose we can assume he is a Jew since he was under the Sabbath rules, but that was likely local law for everyone in the area which was under local Jewish rule. He was just laying in an Asclepion waiting for healing. So what he believed must have been what Christ came to reveal independent of his actual teachings (this ill man would have been ignorant of all that).
Archaeology, as mentioned, demonstrates that Bethesda had seven porticoes, but the fourth evangelist claims that there are five. Most scholars also agree that he was deeply Jewish, and that he had detailed knowledge of pre-70AD Jerusalem and the temple. There must be a narrative reason for this difference, and it must be very important since the author used groups of seven everywhere (seven signs, seven "I am the...", etc).
The temple was modeled on paradise (Eden) with the concept of being in the presence of God. Entry into Jerusalem, or the temple, would be metaphorical for re-entering Eden. Hence the sheep gate was a gateway to eden.. How do you enter this gate if you are paralyzed?
Jesus is "the Shepherd" and "the Gate" in John 10. Bethesda is near the sheep gate (John 5:2). So the sheep gate may be a metaphor for Jesus Christ. He is the way into paradise.
As for the five porticoes, Bethesda is from the aramaic/hebrew "Bet + Chesed" which means "house of grace/mercy." So if John is intentionally ignoring the number seven (the true number of porticoes), what are the five pillars of God's house of grace that provide access to the sheep gate through the son? I read this as the Torah/Pentateuch/Law; the five books from Genesis to Deuteronomy.
If Christ is the word made flesh (John 1), this certainly means, amongst other things, "the law/torah/pentateuch" in human form. Here, Jesus is the sheep gate to paradise, the shepherd, and the five porticoes made flesh. That would be a solid metaphorical reading. Also note that the woman at the well has five husbands (John 4) and Jesus feeds the five-thousand with five loaves of bread (John 5), more metaphors for the Torah.
I would also compare what the man says in response to Jesus' question with John 1:12-13, "12 But to all who received him, who believed in his name, he gave power to become children of God, 13 who were born, not of blood or of the will of the flesh or of the will of man, but of God."
The man says (John 5:7), "No one can help me (will of man), and I cannot do it on my own (will of flesh)."
For me, John 1:12-13 lays out the central thesis of John. This man at Bethesda demonstrated a realization of this and was thus "made whole." It's a submission to God. Realizing that there is nothing... absolutely nothing... that you can do on your own to be made whole and no other human can save you of their own will. You can't "accept Jesus as your personal savior" on your own or with anyone's help... not anything. Give up hope for entering paradise by your own, like this man did, and then the kingdom of heaven is laid out upon the earth (and you can't do this because you want to, that would be hope). Sounds counterintuitive, but the exegesis later in John 5 describes exactly this. Christ does nothing of his own will, but only the will of the father through him.
(John 5:19) "the Son can do nothing on his own, but only what he sees the Father doing; for whatever that one does, the Son does likewise."
John is careful to not imply that Christ has any will of his own. This is in contrast to the synoptics where, in Gethsemane, christ has his own will, but will accept god's will (not my will, but your will be done). For John, there is absolutely no "my will" in Christ.
The "child of God" (John 1:12), which we each can become, is a conduit for the will of God and has no will, hope (of his own), or merit/value as an individual self. As in Philippians 2, he is emptied of self. As in 1 Corinthians 13, he "hopes all things" not a specific thing, which is a fascinating way of saying "no hope" or "hopes what happens." That is some terrifying stuff. For me, it is way more terrifying and wondrous than if someone actually healed some old man two-thousand years ago as the literal reading implies. Note that these two references to Pauline texts (the Carmen Christi of Phil 2:6-11, and the Agape Hymn of 1 Cor 13) are likely very early Christian hymns integrated into Paul's letters and not written by him.
I take this as pointing out that it is exactly the idea that we can act independently of our own "free will" that is sin, our "diagnosis." The Truth is that none of us have free will, but it is our condition to be filled with the delusion of free will which is exactly the knowledge of good and bad (the tree in eden). The knowledge that we are moral agents on our own capable of judgment or of being judged. And there is nothing we can choose to do of our own free will to realize that we don't have free will. It is only when we are convinced of the delusion of our independent will or the will of others, that we are "made whole."
Frequently in John you find the idea that when you believe in Christ, you will not be judged. cf. 3:18, "Whoever believes in him is not judged (κρίνεται), but whoever does not believe stands judged (κέκριται) already because they have not believed in the name of God's one and only Son."
What does this mean? One who understands Christ is purged of the fruit of the knowledge of good and bad, the fruit of judgment (that the world "should" be different than it is - hope). The one that doesn't understand the self-emptiness of children of God stand judged by the delusion of their own will... the knowledge of good and bad.. judgment. John does not say that we will be "judged well" except by another redaction in John 5:29 that is entirely at odds with the rest of the gospel and contains language found nowhere but in John 5:29 and John 3:20 which I believe were moralizer additions along with the other redactions (They are the only places that the concepts of good (ἀγαθὰ) and evil (φαῦλα) appear in the gospel). They are just tainted with that nasty knowledge of good and bad that ejected us from Eden in the first place and to which christ points out an antidote via hopelessness.
Or at least, that is one reading. I absolutely love this story. I think it contains the entire gospel.
I also think the insertion of John 5:3b-4 was from a redactor that didn't have the first clue what the gospel was trying to say. I believe they were trying to place the cause of this supernatural healing in the prevue of God, but I don't think that the "troubling of the waters" needed to be caused by God and it creates several theological problems (like why God would create this competition for healing). There may have been some worries about this as an Asclepion (temple to Asclepius the physician God), which the archaeology supports. The archaeology implies that there were two pools and some scholars have deduced that it may have been periodic filling and dumping between the spring fed pools that caused this "stirring" of the waters.