You think we've got problems: the play opens in the middle of a food riot. See, the lower class plebeians think the upper class patricians are hoarding all the grain and starving them. They've got one guy in particular to blame: Coriolanus, who's a major military war hero. Before they can take action, he's called away to fight the Volscians, who are threatening to invade Rome.
During the war, Coriolanus pretty much single-handedly saves Rome from the Volscians, which makes it kind of hard for the plebeians to justify killing him. When he runs for political office, they vote for him out of obligation—but they're not happy about this.
Snobby politician versus hungry, dissatisfied voters? That's some conflict all right.
If you think your Congressperson is bad, check out Coriolanus: he insults his voters, gets exiled from rom, and then joins forces with his former enemies to demolish his hometown—where his family still lives. Yep, worst politician of all time.
Coriolanus is exiled at the end of Act 3, Scene 3. Seems like a good place for a climax to us.
Coriolanus and his new army are a nanosecond away from totally crushing Rome when his family shows up and begs him for mercy. After some dramatic back and forth, Coriolanus agrees to arrange a peace treaty between the Volscians and the Romans. Awesome for Rome but not so much for the Volscians, who are pretty irritated with Coriolanus for going all soft and not wanting to kill his own family.
At this point, the writing's on the wall—and we can read it from here.
We all know what's going to happen, and Shakespeare doesn't waste a lot of time getting there. When Coriolanus returns to the Volscian city of Corioles, he's immediately accused of treason and stabbed to death.
Talk about a resolution.