I attempted to edit a comment close to the 5 minute timeout and was denied the opportunity to Save. I cancelled and added a new comment.
While I was watching, the edit link of the previous comment didn't go away until it said I edited it 7 minutes ago.
IMHO the edit link could go when it says edited 5 minutes ago, or at least by the time it says 6 minutes ago.
I've changed this to a feature-request because the test comment I added to this question still shows the edit link 10 minutes after I added it. Clearly the link is not currently removed until a page refresh.