What does Romans 3:5 mean?

For the third time in a row, Paul asks a question of himself, as if challenging his own statements at the end of Romans chapter 2. There, he wrote that all people, both Gentiles and Jews, will be judged by God for their sin. Jews will not be spared God's judgment because they have the law or have been circumcised. Those things matter, but all Jews have broken the law just as all Gentiles have been sinful.

Now Paul's imagined questioner asks a more pointed question. In essence, he asks, "If God's righteousness is revealed by our unrighteousness—by our sinfulness—why would God inflict His anger on us? Isn't that unfair? In fact, doesn't that make God Himself unrighteous?" Put another way, "If our being bad makes God look good, why is God angry with us? Why would He punish us, especially those of us in His chosen people Israel?"

Paul includes an aside here, clarifying that he is speaking from a purely human perspective, using a human argument. Many translations put that last sentence in parenthesis to show that Paul is breaking character from this questioner to make it clear to his readers just how ridiculous this question is. This is also intended, by Paul, to clarify that this is not a statement or teaching which he, himself, is making. Rather, this is a point Paul is posing simply to clarify what he is not saying in this letter.

Paul will answer this imagined question with a resounding "no" in the following verses.