This should go away as you get stronger. A 5 mile ride will soon feel like cake, even if it is slightly uphill. In the meantime, try using a lower gear and spinning at 100 rpm. Don't have to pedal 100 rpm all the time, just some of the time. Make sure your seat is high enough, a too-low saddle is tough on the knees and quads. Not sure how you are pulling up using quads, but think more about pulling back - like if you are kicking something with your heel.