This discussion mentions the 5 minute time limit:
Why is the time limit for editing comments only 5 minutes?
The discussion mentions the reasons for and against the time limit. The designers are aware that the behavior for comments is inconsistent with the rest of the site (and this is a "feature"). You can edit SE Qs and As for much longer, like Wikipedia.
The comment edit time limit caught me by surprise, because there is not much warning about this "feature". Perhaps for lower-traffic parts of SE, the time limit can be increased without substantial loss in consistency of the discussion (which is one of the reasons for the time limit).
Workaround:
I often edit the Qs, As and comments in an editor, which has no surprise lockdowns after 5 minutes, before posting them on SE. If you have a favorite editor, you can often save time that way too. Posting from the editor to the SE then requires only a few clicks of the mouse and little typing. Of course, for people whose posts are always short and who make no typos, this workaround is not needed.