What is the meaning of Romans 5:13?

13 (For until the law sin was in the world: but sin is not imputed when there is no law. (Romans 5:13 KJV)

William Burkitt’s Commentary

Having asserted the doctrine of original sin in the former verse, Apostle Paul prosecutes and pursues it in this and the following verses: asserting, That it is evident all have sinned, because sin was always in the world; not only after the giving of the law by Moses, but also before, even from the beginning of the world to that time.
As if the apostle had said, There was certainly a law given before there was a law written: a law given to Adam, before a law written by Moses; now this law was either the law of nature written in Adam’s heart or the postive law of God given to Adam, against which law men were capable of offending before the law of Moses was written; otherwise, sin would not have been imputed to them, for sin is not imputed where there is no law.”
Learn hence, That God, having created man a rational creature capable of moral government, is by immediate result, his King and Governor, and has ruled him from the beginning by a law, yet not barely by a law, but by a covenant, with promises and threatenings annexed, rewarding him for his obedience, and punishing him for his rebellion.