It's the "Fastest Gun in the West" problem and is considered fair here, as long as you use the 5 minute edit window wisely and make your answer very good ;)
see: Fastest Gun in the West Problem
I deliberately left this quick answer short for a while, just for the irony, (sorry! ;)) now I'll try to answer some more of your question - though technically this may be closed as a duplicate I suppose!
The 5 min window can also be used wisely, in my opinion it doesn't put people off from answering but instead encourages them to improve their own answers or add to/expand on the first one so the question asker in fact gets the best of both worlds, so IMHO it is also "legit" or "right"
As long as the OP (or others for that matter) are not too quick off the mark with edits, downvotes or disparaging comments it can work very well in the question askers favour.
Where it falls down, though this doesn't happen often and is "editable" around, is when the question is edited, making the answer look a bit out of context, in which case further edits are needed, if the "fastest gun" is then completely wrong they will usually delete or keep editing until all Question edits are covered - note if this happens to me I don't delete content from my answer (which would be visible in revisions anyway) I give updates explaining the "change" in thought process it helps others who don't know to look at the revisions that there was some work went into getting to the best answer for Question Asker - unfortunately some don't get it and think that the "right" answer even if it's a complete change from their original "Fast" answer should get the votes/tick
Fastest Gun answers depending on who they're from should indicate to the questions askers that someone has committed to answering their question and encourage them to "engage", via comments, if they want the best answer they can can get
So the Fastest Gun answers requires a bit of maintenance too.. hardly cheating, just a different form of "responsibility" from constructing a longer, well thought out/formatted answer immediately.. though there are definitely times when the latter is the better option!