If you click on "edit" on one of your comments before five minutes have expired, you can edit the comment and then try to save it. But if five minutes expire before you click on "save", you can't do it. And you can't see the clock! I find this somewhat obnoxious. Is it possible either to make the clock available or to allow saving comments if editing begins before the time limit expires?
You can "see the clock"; prior to editing, mouse over the time of the comment to see the exact UTC time in seconds the comment was originally posted.
The courtesy editing window is 5 minutes, both for comments and for posts (though the handling is different).
Remember that comments are meant to be little more than "post-it notes" on the units of real work in the Q&A system, questions and answers, and as such they have limited functionality by design -- less formatting, limited space, no revisions, etc.