Romans 5:20 — Moreover the law entered, that the offence might abound. But where sin abounded, grace did much more abound.
The purpose of the Law was to show man's guilt and his inability to achieve righteousness by his own efforts.
Grace didn't remove the Law, but satisfied it.
This verse is connected back to verse 13 — the Law came in addition to sin.
The Law doesn't make men sinners, but it makes them transgressors.
Abound — Sin in abundance was overwhelmed by grace in super-abundance.