When two people have private conversation after 5 minutes it is not possibile to edit the post. I see no reason for such limitation. For example, after hour ago, if I check what did I wrote, and saw grammatical or orthographic errors I can not correct any more. My proposal is to abolish time limitation in conversation editing.
If it doesn't hurt the bandwidth load, or have any other adverse effects on the site, I concur with this suggestion.
In truth we would like to limit post-editing as well. Much too often on the Internet, people change their opinions or revise their posts after they have been said, altering the sense of the original conversation. Some time should be allowed to fix any typos we may have, 10-15 minutes or thereabouts, but afterwards the post would stay unalterable, except by a moderator. That is a long-range goal, however, and there are no plans to introduce it soon. A limit to conversation-editing is already in line with this objective however, and shouldn't be removed; the only item to adjust being the timeout which should probably be longer than 5 minutes like you said.
I agree with the administrator here. A maximum of 10-15 minutes to correct typos is more than enough. The same should happen in PM.