You may be in luck and have a simple 2 direction motor with a starter winding. If so, what you may have is a common run winding wire, and one wire for each direction ( thats 3 of the wires that are related .) The other 2 wires will be the starter windings, that would need to be powered in the direction you want the motor to run in. On simpler machines, the transmission/pump does the agitation in one direction of the motor and spin/pump in the other.
I had a old washer back in my college days that was dumped because the control timer was wrecked, I got it for free since the timer control was too expensive. I wired it up with a DPDT switch and a momentary push button for the starter windings. I used a 2 dollar kitchen timer for timing how long the machine had run.
If you know the model of the machine it came from, the maker may have wiring daigrams available on the net. Often they were on a piece of paper glued to the inside of the amchine also.