Small Engines (Lawn Mowers, etc.): Agway Riding Lawn Mower, briggs and stratton, putts out

Question
I just received a Agway (Murray) 12/40LT riding lawn mower. It has a I/C Briggs and Stratton 12hp engine in it.

The machine starts up great turns right over putts out some smoke from the exhaust then just run fine for about five minutes or so and just starts shaking and then dies out completly. Try to start it up again and it just keeps turning over and will not start at all... Then the next day I come back battery is all charged up it fires up again without any issues!! I have to wait a day to fire it up again for it to have the same 5-6 minute life

Gas is new, oil is new, took out the spark plug it looks in decent shape cleaned it off and put it back in (but could be replaced). I took the air filter out cleaned that out nothing blocking the air way.

Any help or step by step instruction would be great. I am a newbie to small engines.

Thanks

Answer
This could be a carburetor problem, but also could be a worn engine. The only way to diagnose this is a leakdown tester. I guess since you probably don't have one, I suggest you check the carburetor and clean it thouroughly, if this doesn't help you may need to take it to someone who can test it with a leakdown tester.