Conversation so far:
What point was considered the height of their commercial success?
1983 saw the release of Speaking in Tongues, a commercial breakthrough that produced the band's only American Top 10 hit.
Was that their best selling album?
Speaking in Tongues.
Did they break up after this album came out?
It took until December 1991 for an official announcement to be made that Talking Heads had broken up.

Question: Why did they break up?
Self-contained rewrite: Why did the Talking Heads break up?