What is the reasoning behind this?
The real problem is that, second class citizens that they are, comments do not have a public revision history.
SE lets you edit pretty much everything else at any time because there's edit accountability: At any given moment, you know who changed what, when, and why. This isn't the case with comments — this is why comments can no longer be edited after the standard grace period.
This isn't an answer so much as a nag -- I have a little issue with this 5 minute rules. I accidentally hit save on my comment right after I started one. No big deal, edit. Typing, typing, typing, no warning from the site. Save, and wham, edit not allowed. Aw, come on!
If you're really going to enforce this, either
- give a warning while editing the comment (like a doomsday counter) so that the user is informed, or
- just give a grace period - like you can't start an edit after 5 minutes have passed, but you can save the edit for 15 minutes from the original post.
As others have noted, comments are ephemeral second class citizens with no revision history. That's a really complicated way to say that they are meant to be temporary aids to posts rather than primary content. If the content of a comment is so important that it needs editing for improvement over a long period of time, perhaps it needs to be written up to be a full post. If the context has changed and a comment needs to be tweaked to reflect the new situation, remove the old comment and write a new one. (You can even copy/paste the old one before deleting if you want to start with that.)