That's just way too close to departure time. The GA's job is to get the door closed and the jetbridge retracted on time. Period. Anything else has far lesser importance. And getting on the computer to process 5 more pax with only 5 minutes before departure counts as "something of far lesser importance." It doesn't matter if you are PLT.
It would have been different if you had arrived 20-25 minutes before departure. Remember, technically, if you are not at a domestic* departure gate 15 minutes before departure, you could (and likely will) lose your seat.
It was YOUR responsibility to make sure that you had sufficient time to make the NWA->AA connection.
* "Domestic" in this situation means any flight that operates entirely within the USA.
Although, for me personally, I would never arrive at the gate later than 30 minutes before departure for a flight to Hawaii or Miami, a non-stop transcon, or ANY flight operated with a widebody aircraft. It's just too easy to be left SOL by an overzealous (yet all-powerful) GA.