SchmutzigMSP outlines the general rule of thumb for NW door closure procedures.

With the thousands of flights on any given day, it's inevitable that a flight will go out without pax that should be on it because of a delay on an earlier flight, etc. It's unfortunate that this happens, but it's just a part of the airline world, and would be something that happens on any airline. So while we've all been in that spot and know how aggravating it is to watch as our flight pulls away from the jetway and gate, I'm afraid there won't be much NW will do in this situation for you.

Perhaps you could ask why the time is 5 minutes and not something smaller. IIRC, SW closes its doors 1 minute prior to departure time.