You will have to document the Resistance-Values between all of the Wires and post them here.
The Resistance-Values may be very low numbers, so You will need a Digital-Multimeter.
Nothing can be done until a good guess can be made as to what each wire goes to.
It may need a "Motor-Start-Capacitor" to start-up by its self.
It may also have 2-Speeds.
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Here is a guess based on some experience. It is a fan motor from a window-mounter air conditioner, and it has three speeds, high, medium, and Lo. And I will guess also that the white wire d the common. So to verify that you will need to measure the resistance between the white wire and each of the other wires. For a verification and try-out, attach a powr cord between the white wire and whichever has the highest resistance. For testing you should remove the fan blade to reduce the chance of injury. Then momentarily apply power and see if the motor runs. It is probably a shaded pole induction motor, AC fans do not generally use motors with start switches.