You said it's a 1990 furnace. Is the high limit cut-off problem a new event? I assume that before the 5 minute cut-off of the burners that the main blower does start and that hot air is flowing from the supply registers when the high limit is exceeded. If you have done nothing to the ducting since the furnace was installed and this limit problem is a new event, then I would say the ducting, supply and returns, assuming all are open, are not the problem. Too big a furnace would only cause short heating cycles since the installer would have sized the ducting, returns and supplies for the furnace BTU and blower air flow requirements. However I would check the ducting in case there are any bends (especially with flex ducting) that could be impeding air flow.
If all ducting looks good then there could be 2 possibilities. First the limit switch is bad. It's a piece of metal that expands with the rise in temperature. After so many expansions/contractions, the metal fatigues. Make sure you replace it with an identical probe. I assume you watched the temperature dial on the limit switch pass the high limit setting and also watched as it passed the blower on temperature and heard the main blower start.
The second possibility is the blower is not giving you the required air flow (cubic feet per minute - CFM). Check the motor and the blower wheel (squirrel cage) for any play indicating bad bearings. Also make sure the blower wheel is clean. Finally you might replace the motor run capacitor. It's 10 years old and it could be failing causing the motor to not generate the CFM it should be giving you. Capacitors are inexpensive and easy to replace so I'd start there.