Who are the dead that the Father raises up, and who are they that the Son raises in John 5:21?
The grand subject of the Gospel of John is Life, and in chapter 5 we find that the law does not bring a person into life.
In this chapter the Lord Jesus, amongst other things, makes plain and emphasizes three times that He and the Father are One (vv. 19, 24, 25), and that the Son does the things the Father has shown Him and "will do greater works than these that ye may marvel." Verse 21 teaches that there is no discord between the Father and the Son.
The whole passage shows the oneness of the Son with the Father when on earth and represents the Father before men in works of grace. The Son quickens (makes alive), but in verse 22 to Him is given judgement. In verse 24 we see the great expanse of blessing for those who have faith to hear the Son of God: possession of eternal life, escape from judgement, and passage from death into life.
Verse 25 moves the view from our side as exercising faith (v. 24) to the sovereign action of the Son which is still going on; eternal life is communicated to the believer from Him, the One who is the source of life. So we find in verse 29 that the believer, because he has life eternal, has the power to do good (a new nature) - such are raised by the Son, as we would say at the rapture (1 Th. 4.) while the wicked dead will be raised for the Great White Throne judgement (Re. 20). The judgement, although in the hand of the Son of Man, will be executed in accord with the "will of Him who sent me."