Okay you have a dual 10cc hydro pump and two wheel motors. Your particular serial range uses JO Plus 50 15W-40, 20W-50 1.7 qts with filter change per cheat sheet here. Later model Z425 that have hydrostatic transaxles used a lot more oil, around 2 gallons and two filters if both transaxle are done.
Can be a drive belt slipping caused either a worn belt or a sticking idler arm. If the idler arm is binding it can act as if the belt is slipping even with a new belt installed. Also check the depth the v belt is riding in the v-pulleys as if it is bottoming out it can cause the belt to slip. This would be the first items to check before hydraulic oil and filter change. If none of this resolves the problem then look at either rebuilding the pump or replacing it. With nearly 6000 hrs it can be any of these items.