How can I get my lawn mower to stay on?

The mower is very new, maybe 5 hours of use. First start of the season I tried to start it with the last season's gas. It would run (it seemed) as long as the primed gas would last. I drained the old gas, filled with new gas and got the same results as with the old gas. I suspect it's not the gas because I never had any problem with previous lawn mowers using old gas. It is a briggs and stratton engine-bolens lawn mower. Any ideas? Thank you