1996 Ford Contour Car Shaking

The car handles okay until I get to about 55-65 mph. In that range the steering wheel starts to shake, and there is excessive road noise coming from the back left tire. After I clear 70 mph and above the handling returns to normal.

I have checked the tire pressures and filled them accordingly (they were all off by 5-6 psi either way). Even after correcting the tire pressure I still have the same problem. The car previously sat in the parking lot of my apartment for a few months while I was out of town (in the Georgia summer), so I'm guessing I just need to get a new set of tires. I just wanted to find out if there was another solution before I spend the money.