STX38 Transaxle problems/won't go in gear

So I've riding around on my STX38 I bought for parts and am now debating fixing it because it runs so darn good. First I don't believe it's a hydro because it's a yellow deck. 1, 2, & 3 all work well except it is very hard to shift into and out of the gears. It feels like the selector is either binding or needs serious lubrication. It seems like the tractor was left out uncovered for at least a year. It will go in 4th sometimes and it will not go in 5th at all--same with Reverse. Has anyone else experienced this? I'm fairly mechanically inclined, so is it fixable or should I just park it and part it like I originally planned? I plan to take a few pics in the next day or too. The hood is nice with minimal signs of wear. Thanks.