Did the shop say there were error codes in memory? What is "resetting" after five minutes? If I was a gambler, I would say it's the Air temp senser or Engine temp senser... or possibly something has been installed on the bike that makes one of these sensers get hotter than the ECM expects it to get. (like something that would divert cool air away from or hot air into the senser area)

My 2003 Heritage would sometimes do nothing when I went to start it. i would smack the seat hard and then it was fine. Sometimes I would have to pull the seat and thump the starter relay. Possibly the main relay is getting hot and discombobulating. Or possibly something is going on with the ignition module. If one of the componets has heaters that will open when they get too hot and the spring on the heater is weak, then it can act exactly as you describe.

In any case, a mechanic should have been able to fix it right the first time.