ESV, 1 John 5:
13 I write these things to you who believe in the name of the Son of God, that you may know that you have eternal life.
John addressed the brothers in the church. He was going to contrast life and death to close this letter.
14 This is the confidence we have in approaching God:
πρὸς (pros)
Preposition
Strong's 4314: To, towards, with. A strengthened form of pro; a preposition of direction; forward to, i.e. Toward.
This is the confidence we have toward God:
that if we ask anything according to his will, he hears us. 15 And if we know that he hears us—whatever we ask—we know that we have what we asked of him.
Ask and it will be given to you (Matt 7:7a).
16 If you see any brother or sister commit a sin that does not lead to death,
The word "lead" was not in the Greek.
committing
ἁμαρτάνοντα (hamartanonta)
Verb - Present
Participle Active - Accusative Masculine Singular
Strong's 264: Perhaps from a and the base of meros; properly, to miss the mark, i.e. to err, especially to sin.
a sin
ἁμαρτίαν (hamartian)
Noun - Accusative Feminine Singular
Strong's 266: From hamartano; a sin.
leading to
πρὸς (pros)
Preposition
Strong's 4314: To, towards, with. A strengthened form of pro; a preposition of direction; forward to, i.e. Toward.
If you see any brother or sister sinning a sin not πρὸς-toward death,
you should pray and God will give them life.
John contrasted life and death.
Was John talking about physical or spiritual life and death?
John used the terms life and death ambiguously on purpose.
If you see a Christian sin and sin, πρὸς-approaching death, but he desires to repent, you should pray, and God will give him life to repent. He will not die in his sin.
I refer to those whose sin does not lead to death.
This sin does not lead to spiritual death because he is repentant.
There is a sin that leads to death.
However, there is a sin πρὸς death.
Was John talking about blasphemy against the Holy Spirit, i.e., the sin of unbelief?
I don't think so. John was addressing believing brothers here.
What was this sin πρὸς death?
It was not any particular act of sin. It had to do with the brother's attitude toward this sin.
What was the nature of this sin πρὸς death?
A brother sinned this sin πρὸς death when he was unrepentant. Perhaps he did not consider it a sin. He would not listen to other brothers' advice about this sin. He would stubbornly hold on to this sin until the day he died.
I am not saying that you should pray about that.
Don't bother praying for this brother. He will never change.
17 All wrongdoing is sin, and there is sin that does not lead to death.
All wrongdoing is sin, yet there is sin not πρὸς death.
18 We know that anyone born of God does not continue to sin;
We know that anyone born of God has the Paraclete dwelling in his spirit. He does not practice sinning stubbornly without being repentant about it.
but he who was born of God protects him, and the evil one does not touch him.
The Paraclete dwelling in his spirit protects him, and the evil one does not touch his spirit.
There are Christians who sin, and sin, and sin the same sin unto death. They will die in this sin. Their spirit is weak and not growing in the Paraclete. They don't think they need to repent of this πρὸς-death sin. There is no point praying for them about this sin.
Are these Christians condemned to eternal death?
No, not necessarily. It is not the unforgivable sin. It is not the sin of (eternal) death. It is the sin πρὸς-toward death. The prognosis is not good. They are heading there. John's last sentence in this letter, he warned them:
21 Little children, keep yourselves from idols.
God will decide who gets to heaven.
What is the sin unto death?
It is a sin that the Christian refuses to repent of in his lifetime. He will not repent even at his (physical) death. This sin will gravely endanger his receiving eternal life after the resurrection. He will likely experience the second death. Don't idolize your sin. It will lead you to spiritual death.