How does Iago's treachery finally work itself out in Act 5 of Othello?
Iago's treachery plays out throughout Othello. We see it working to disrupt relationships, poison attitudes, etc. This comes to a peak in Act V. That's when he tries to kill Cassio, and when he does kill Roderigo. He smears Bianca almost as an afterthought.Acting on Iago's manipulations, Othello kills Desdemona. There's a huge upheaval, and the truth comes out about Iago's lies. Othello tries to kill Iago, but fails. Iago stabs his own wife (cold!), and Othello kills himself in despair over what he's done.
In short, everyone is either dead, has a ruined reputation, or both.
Jealousy is one of the major themes in Othello. In the last scene, Othello is completely devastated when he discovers that Iago has been deceiving him all along. I think that Iago makes an end to his treachery in his final words:
"Demand me nothing. What you know, you know./From this time forth I never will speak word." (5:2, l. 300-301)
Throughout the play, Iago has been secretly tormenting Othello with his lies. I think that these final lines show Iago's last stab at ruining Othello.