When put into drive you can feel the engagement but the engine still skips

This truck has been sitting for about 4/5 years. When it was parked it was said that it had a transmission issue. It is now in my possession, and I got it running, and yes, there is an issue. When put into reverse the engine will skip when you give it gas to try to back up but it won't pull the truck. When put into drive you can feel the engagement but the engine still skips when given throttle. Now, when put into manual first the truck will move fine. And in manual second it will move but not as well.

So, the truck is now in the air with all 4 wheels on jack stands. When I put the truck in reverse the rear wheels will turn backwards, and also turn when given gas. Same for when in drive. Think it's time for a new transmission or should I bother with trying a filter change? I also heard that these transmissions have adjustable bands?

Waiting to hear your thoughts.