Ive never seen a stx38 in person but from tractordata it looks like a peerless 920 in there. First check if drive belt is slipping the pulleys will be polished in the grooves if so. Next check to see if the keys are on the shafts if belt checks out. If they check fine check the keys in the hubs(tires). Someone should come along whos had or wreched on on soon.
The STX were built mainly in the early to mid 90s. The black deck ones weren't as durable as the earlier yellow deck models. Since we're talking at least a 25 year STX, more than likely the transmission is worn out. Have you changed the drive belt recently? Check the tension spring?
If this one is the gear drive model, it sounds like the classic worn out belt. Or the belt has gotten oily from an oil leak somewhere. My STX46 will act like that when the belt gets wet with water. Once dry, it works as it should.
I recommend checking the belt and associated tensioning parts first.