I came across this problem with my friends Honda 5hp fitted to his Shrimper yesterday and think it worth sharing. The engine looks very clean and well serviced but it's history is unknown. It starts easily but quickly labours and eventually cuts out and will not restart. The emergency solution is to remove the engine cover and the engine starts immediately and works perfectly.
The problem is a small corrosion hole in the exhaust manifold that sits below the engine inside the engine cover. The cover fills with exhaust gasses and prevents the carburettor breathing fresh air.
A new manifold is required clearly, but in the short term can the hole be fixed with a metal filler? We will find out...
I have heard of Honda 5's stopping through an unknown cause so this is worth checking out if it happens to you. Remove the cover and see if the engine restarts.
Best wishes
Chris
Kaliope 67