When it does that quickly loosen the gas cap. It could be a vacuum issue building in the tank. If that is it then the cap vent line check valve is either in backwards clogged or the cap internally is clogged. Seem many, many vent issues over the years. They can allude you for a long time until you find them.
Otherwise the only suggestion would be that you are flooding after the 5 min run time. But that seems odd since it starts and runs fine for 5 minutes.
Stator issues can also be really tough to find - they can be fine while cold then fault out when hot but that usually does not give "bogging" conditions it is more of a very erratic and miss fire condition. Would not hurt to go a ohm's / resistance check when it acts up just to eliminate the stator.
Hope those ideas give you some direction to go.