Romans 5:13, “For until the law sin was in the world, but sin is not imputed when there is no law.”
Sin has been in the world since Adam first sinned back in Genesis 3. However, Paul says here that sin is not “imputed” or charged against someone when there is no law. In other words, sin cannot be counted against someone if there is no law for them to sin against. This seems appealing, but what does this do for those who lived between the time of Adam and Moses? Obviously, some were punished according to their sin during this time period (e.g. Cain, Noah’s contemporaries, Sodom and Gomorrah, etc.).
This is a hard passage, but we must remember that it fits within greater contexts (this passage, the book of Romans, and the biblical narrative). Although this verse is not complete with considering these other context (especially v. 12-14), Schreiner offers helpful insight by suggesting that in verse 13 (along with 14), Paul is showing the extent to which death reigns. He says:
How then do we explain verse 13, which says that sin is not reckoned apart from the law? The purpose of that verse is to explain that apart from Mosaic law sin is not equivalent to transgression. This is confirmed by both Rom. 4:15 and the present context, for Paul notes explicitly in 5:14 that Adam’s sin was different in kind from those who lived before the Mosaic law in that he violated a commandment disclosed by God. One could still object that this distinction is rather trivial since those who do not “transgress” the law are punished with death anyway (e.g., the flood generation). In response, I would say that Paul’s objective was twofold. First, the power of death is so great that it exercises its dominion over people even if no law exists. Second, violating a commandment revealed by God increases the seriousness of sin in the sense that the sin is now more defiant and rebellious in character. This point accords with Pauline conception that sin increases (5:20) and takes on a sharper profile (7:7-11) through the law.
This explanation is helpful in that it stops us from assuming that those who lived before Moses were excused in their sin because they had no law. We also want to be careful not to minimize the effects of Adam’s sin, which had an awful effect on all who came after him, whether with or without the law. Luther sheds light on the former point:
The meaning of the passage, then, would be this: Until the law sin (which, to be sure, was in the world always) was not imputed; in other words: it was not imputed or known until the law came; the law brought it forth – not in the sense that it called it into being, for it was there before, but in the sense that it called it to the attention of the mind so that it could be known.