My 435 John Deere lawn mower will start fine and run fine for about 5 minutes, then it starts spluttering like it is flooding out and won't run. It keeps this up for about 15 minutes, then it will take off and run fine for the next 2 hours that it takes to mow my lawn. What is wrong with it?

Sounds like you have a small particle of something in the fuel system. When it eventually finds it's way to the fuel valve it floods.

My 435 John Deere lawn mower will start fine and run fine for about 5 minutes, then it starts spluttering like it is flooding out and won't run. It keeps this up for about 15 minutes, then it will take off and run fine for the next 2 hours that it takes to mow my lawn. What is wrong with it?
This sounds like mine. I noticed my fuel lines were tightly installed. Meaning tight corners and when the motor compartment got hot I believe my fuel lines were getting soft and pinched at bends or corners. I installed new lines with some slack for bends. No problem ever sense.