The five minute window helps in fixing some comment mistakes. Comment edits that drastically change the content, alter the flow of the comment thread. But, correcting mistakes in comments after the five minute window requires deletion of the original comment.
My proposal is to allow comment editing after the five minute window, but that the edits must be approved in a manner similar to having edits to questions and answers approved when your reputation isn't high enough.
This will let comments be grammatically corrected, but prevent changing of their meaning.
Here are some references to older pertinent discussions on comment editing. These are from 2009.