He may just get tired after 5-10 minutes - he's still pretty young and a lot of highchairs don't give the support they should. Does yours recline at all? That helped my dd around that age, but also left her pretty far back from the tray.
I'd just keep doing what you're doing, and every time he sits for 5 min he's building the strength to go longer. He may suddenly start to enjoy it more in another month when he can eat finger food - that made a difference for Rachel, because she had something to do besides just open her mouth.
There are also suction-cup toys that you can stick on the tray (if he can reach it), and that may distract him long enough for you to eat.