((in re: John 5:25))
some of the immediate context:
For just as the Father raises the dead and gives them life, even so the Son gives life to whom He is pleased to give it.
(John 5:21)
Very truly I tell you, a time is coming and has now come when the dead will hear the voice of the Son of God and those who hear will live.
(John 5:25)
Do not be amazed at this, for a time is coming when all who are in their graves will hear His voice and come out — those who have done what is good will rise to live, and those who have done what is evil will rise to be condemned.
(John 5:28-29)
and the greater context of this whole oration, is
Jesus gave them this answer: “Very truly I tell you, the Son can do nothing by Himself; He can do only what He sees His Father doing, because whatever the Father does the Son also does."
(John 5:19)
answering what? answering the charge against Him because He was doing His works on the sabbath - saying, the Father is always working, and He, too is working.
the context even larger than this, is that it is in the book of John -- and yes, as you say, everything in John is 'proofs' of who He is ((re: John 20:30-31)) -- so yes, it is proving that He is the Messiah, the Son of God, God Himself manifested in the flesh. every bit of John is demonstrating that Christ is God.
but those few verses i picked out near John 5:25 -- doesn't He say, those dead who hear His voice and live, are those to whom He grants life -- for He gives it to whom He is pleased to give it ((v.21)), and that tho all are resurrected, some are resurrected to life, and some to judgement - so that those who hear His voice and live in v.25 is not 'all the dead' but those to whom it pleases Him to give life? since some are raised not to life, those very ones being the ones who do not hear His voice ? ((re: John 8:47))
such that there are two different kinds of 'hearing' being spoken of here -- in vv. 28-29, all the dead hear, and are raised. but in v. 25, those who hear are all raised unto life, tho in vv. 28-29 not all are raised unto life, but some to judgement and eternal death.
Whoever belongs to God hears what God says. The reason you do not hear is that you do not belong to God.
(John 8:47)
this is a difficult passage to swallow -- some say, 'the reason you do not belong to God is that you do not hear Him' -- but that is not what Christ says. He says the reason those who do not hear, do not hear, is because they do not belong to Him ((and this is the kind of hearing that results in life, not the broad kind of hearing that may be in-one-ear-and-out-the-other)).
it says, His sheep know Him and hear His voice. it does not say, those who hear His voice become His sheep. it says they already belong to Him.
AND
all of this in John 5 is specifically answering the charge against Him of doing His works on sabbath. it is both demonstrating that He is the manifestation of God in flesh, and also all related to His working on the day called the day of rest.
how?
is it not so, that if we are found in Him, and He does nothing of Himself but the Father working through Him, then we also likewise can do nothing of ourselves, but Christ working through us? if this is true -- then how is it that we, being dead, hear His voice and live? that 'hearing' would be a thing we do tho we can do nothing of ourselves - is it not His own power within us, hearing, quickening, and raising to life, so that we can walk in Him? because the life in us, is not us, but Him -- He is 100% "The Resurrection and The Life" ((re: John 11:25))
how is this all about working on the day of rest? true rest is in Him - He who is my rest