[Ombudsman]

According to AirTran's website the cutoff time to be at the gate is 10 minutes prior to departure time. If all other passengers were seated, overhead bins closed, etc. @ 5:10 it is quite conceivable the gate agent closed the flight out in the computer, delivered the final paperwork to the crew, and got the door closed within 3 minutes which is the posted departure time of 5:13. Unfortunately I don't think the OP has a case as she indicated the aircraft departed "at least 5 minute early" so we can only assume she was at the gate around 5:15. I've missed flights myself due to various reasons (traffic, long TSA lines, late hotel shuttles, once I mistook the "boarding time" printed on the boarding pass for the actual departure time) but the bottom line is if one does not make the cutoff time either outside at the counter or at the gate they are at the mercy of the airline and their rules/terms. The OP complained of additional gas/tolls and lost wages due to returning to BWI one day later but never stated the airline charged her to change her reservation to the following day so at least ATA made an exception to their own rules and waived the $75 change fee and any additional fare which, rebooking last-minute, could have been expensive.