God’s impartial judgment of everyone, Jews and Gentiles, brings to the fore a reference to “wrath” in Romans 2:5:

1 Therefore you have no excuse, whoever you are, when you judge others; for in passing judgment on another you condemn yourself, because you, the judge, are doing the very same things. 2 You say, ?We know that God?s judgment on those who do such things is in accordance with truth.? 3 Do you imagine, whoever you are, that when you judge those who do such things and yet do them yourself, you will escape the judgment of God? 4 Or do you despise the riches of his kindness and forbearance and patience? Do you not realize that God?s kindness is meant to lead you to repentance? 5 But by your hard and impenitent heart you are storing up wrath for yourself on the day of wrath, when God?s righteous judgment will be revealed. 6 For he will repay according to each one?s deeds: 7 to those who by patiently doing good seek for glory and honor and immortality, he will give eternal life; 8 while for those who are self-seeking and who obey not the truth but wickedness, there will be wrath and fury. 9 There will be anguish and distress for everyone who does evil, the Jew first and also the Greek, 10 but glory and honor and peace for everyone who does good, the Jew first and also the Greek. 11 For God shows no partiality.

Wrath here refers to the day of wrath — the day of God’s judgment. Whether or not a person experiences God’s wrath depends on works (v. 6).
Since the alternative to wrath is “glory and honor and immortality” (7) and eternal life, we are led to conclude with confidence that “wrath” here is “eternal wrath.” A post-mortem condition in which a person whose works are inadequate (because they are “self-seeking” and do not “obey the truth” and do “wickedness and evil”) experiences God’s wrath. The text does not say how long one will endure God’s wrath.
This “wrath and fury” leads to “anguish and distress”; those who escape God’s wrath experience “glory and honor and peace.”