Romans 5 is clear. The reason we die is because of sin. No sin means no death. I know that we all sin so this is somewhat of a moot point. Nonetheless, it is true that if someone didn't sin, they wouldn't die. That is precisely why Christ didn't stay in the grave.
1 John 3:4 says sin is transgression of the Law.
Believing on Jesus is a commandment (Law) (1 John 3:23).
Repentance is a commandment (Acts of the Apostles 17:30).
Believing in the gospel is a command (Mark 1:15).
Not murdering is a command. If one hates their brother they are like a murderer and no murderer has eternal life abiding in them (1 John 3:15).
Not lusting after a woman is a command and the consequences for doing so is being cast bodily in hell fire (Matthew 5:28-30).
The law Paul speaks of is the Old Law given to Israel and not God's Eternal Moral Laws (like do not murder, do not steal, do not covet, etc.). However, the ceremonial laws like the animal sacrifices, the dietary laws, the Sabbath, circumcision is what Paul condemned for a believer if they seeked to do such things so as to be saved (or continue in salvation). Paul says in Romans 3:1, what profit is there in circumcision? In Galatians 5:24, Paul says, if you seek to be circumcised, Christ will profit you nothing. So Paul condemned going back to the old ceremonial laws of the Old Testament; Paul did not condemn people for not murdering, or not stealing, etc. That would be silly.
So saying, "we all sin" is not correct. Not all Christians live like heathens or unbelievers.
Philippians 2:15 says,
"That ye may be blameless and harmless, the sons of God, without rebuke, in the midst of a crooked and perverse nation, among whom ye shine as lights in the world."