Hi,
I don't know these outboards very well. We had several of them in a rental fleet on a small lake but I didn't work on them much. I remember that they seemed very reliable though except for one thing: that danged recoil starter. They broke constantly but it was mostly because of the neutral lockout. The customers would forget to put the trans in neutral and, when they were ready to go again, "LOOK BOB, THIS DURNED THING IS LOCKED UP!!...WHAT ARE WE GONNA DO???..
THE SHORE IS 20 FEET AWAY!...WE'RE GONNA DIE!...."
At which time they would haul back in a panic or a rage and give it their MIGHTIEST PAUL BUNYAN (Vin Diesel if you prefer) YANK and... VOILA... problem solved!
Motor starts right up and didn't even hear that little "pop" as the pull start neutral lock-out mechanism snapped and broke.
Because?? It was plastic. As are many things on outboards these days.
I don't recall exactly that "failure" caused the pull start to begin giving trouble but I remember that we just had lots of problems with them. The company knew that I was probably in a different county most days and because we were a rental company, we HAD to have the neutral lock-out working properly. So...they just kept several in the store and would have the docklands change them out when necessary.
I think I actually ordered the parts and repaired the first one on the 2 week old shiny new outboard but don't remember the particulars
I think I do recall that a new plastic pinion gear was part of the replacement "proceedure". But...memory is fuzzy there...
...and here.....
...here and there actually....
Anyway...
I can't say why you have that water leak...I would suspect a bad flush valve if it were on a larger twin but I don't recall the 5hp having one.
The stalling after one minute run time might, I reiterate MIGHT, indicate that it's not cooling properly. But it could still be the carb too. If she seems to be a bit on the rich side, maybe you missed the float set up a tad?
Anyway, good little units but that pull start was a manufacturing mistake in my opinion.
Good luck.