Hi Kelly. Before doing anything , I would check compression. I see a lot of the older two strokes with worn/damaged motors and it's no use doing much of anything until you make sure that the top end is in good shape. Compression should be a minimum of 130 lbs. and be even on both cylinders.
There are a number of reasons that could cause it to stop running the way you describe. Have you checked for spark when it stops running? Take a couple of extra plugs with you and and check for spark next time it quits.
You mention that it sat for 5 years without being winterized. This is probably where the problem lies. It's very common to see carb problems on watercraft that haven't been winterized for 1 year. After sitting for 5 years , I would expect to find the carbs very gummed up and maybe some bad diaphragms. etc.. This would be a job for an experienced mechanic, as the carbs would need to be completely disassembled, cleaned and pressure tested.
Could be other problems also, but that's my 2 cents. Good luck!
onemadmonkey
July 2008