Romans 5:20 would have shocked the observant Jew of the 1st Century. “The law was added so that the trespass might increase.” Oh, really. That is why God gave the Torah? Here is where it becomes clear that the New Perspective has a little more to say.
I have said before that Paul’s fundamental starting point changed everything: he began with Genesis 12, the promise to Abraham, where his “dialogue partners” began with either the Torah in general or with Exodus 19–24 in particular. Paul read the Bible through the idea of promise, his sparring partners through the idea of Torah.

Torah was the gift of God to Israel. Torah reflected election. Torah gave Jews a moral advantage.
Did God give the Torah for the purpose of revealing sin? Or did God give Torah and one of its implications was a knowledge of sin? The former. Pretty hard to read hina any other way. (Wright agrees.)
Paul sees God’s gift of the Law as God’s grace to Israel to reveal that Israel, too, had a sin problem like the rest of the world. Torah, instead of giving the chosen people a source of pride for its moral advantage, gives that same elected people an acute awareness of its sin.
It is not hard to find examples of this: think of a time when you were unaware of somethig, but once aware, you realized from that point on that such a behavior was wrong. Speeding on a highway, for instance. We might go to fast, but we know it is wrong.
Now the big picture here is that Jewish privilege is ended by Torah not entailed by it. This is not just a general “knowledge brings knowledge of sin.” The Torah entered into history with Jews, not into history for all humans at once. This has to be said first. The entailment is clear: the Torah brought knowledge of sin for Jews. Instead of simply a privilege of election, Torah levels all.