Small Engine Problems? Ask an Engine Mechanic for Answers ASAP
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I think you may be working with two separate problems. Let's start with the hard to start issue, this is almost definitely a compression release issue. It is within the valves so all we need to do is readjust your valves and get everything back in spec.
Your valve specs for this engine are; Intake .003 - .005 inches, Exhaust .005-.007 inches.
Here is the procedure
Remove your spark plug
Remove your valve cover, and then set your engine to top dead center (both valves will be closed and rockers should be slightly loose) Using a pencil insert it into the spark plug hole and mark it (move the engine back and forth to make sure that the piston is at the top of it's stroke). Remove it and make a second mark one quarter of an inch up the pencil. place it back in the plug hole and turn the engine until the pencil drops the quarter inch you marked.
Now you can adjust your valves to with in the recommended specs
Adjusting them is fairly easy, you need a feeler gauge to slide between the rocker arm and the valve spring. (see picture)
On the rocker arm there is a nut and a torx or allen head bolt in the center. Loosen the locking nut and adjust the center screw until the feeler gauge has a slight drag on it when pulling between the rocker arm and spring. Once it is set tighten down the lock nut and then do the other cylinder. Double check all valves before starting
The dieing after 3-5 minutes would be your second issue. You can not address this issue until you get the valves taken care of. In a perfect world adjusting the valves would fix both problems, bu this may not be the case and I wanted to address the known problem first. Once your valves are set we can test the engine. If everything is fine (and it may be) then we are good. If the engine is still dieing then I would start by looking at the ignition system and see if the spark is stopping after warm up.
Let's start with the valves and hope that both problems are ties together and the valves are causing the overheating
If you have a single cylinder then you only need to do each valve separately.
I just reread what I wrote, it should read "then do the other valve" sorry for the concussion