What does Romans 2:5 mean?
Paul is calling out all those who sit in judgment—in their thoughts, words, and actions—over the sinfulness of others. In the previous chapter, Paul described in great detail how a refusal to acknowledge God leads to an avalanche of sinful lifestyle choices. In this chapter, Paul has clarified that all of us participate in sin. That error is not merely connected to those thought of as the most sinful in a particular culture.To assume that God will not judge our own sinfulness, because He shows kindness to us in this moment, is a dangerous presumption. God's kindness now is meant to lead us to turn from our sin, not to continue in it. In fact, Paul now writes, those who refuse to repent from their sin are storing up God's wrath for ourselves. God will express that wrath on the "day of wrath," the day when His righteous judgment will be revealed.
None of us should make the mistake of thinking that just because our sins seem smaller, we will be saved from His wrath toward our sin. Nor can we assume that our relationship with God is more special than that of other people. On the contrary, as Paul is saying, all people are guilty and deserving of God's wrath. Our good deeds cannot and will not save us.
It's critically important to continue to follow Paul's train of thought in Romans. He's not done, yet. He will eventually show that there is, indeed, a way to be saved from God's wrath (Romans 3:22–25).