I am replacing a defective A/C condenser motor (K55HXMHS6410) which has three wires coming from the motor (yellow, black, and brown). The new motor I am trying to reinstall is a 554 outdoor condenser fan motor which has a black, white, brown/white, brown and red wire. How do I reinstall the new motor which has different wiring to my current A/C unit.

Are you sure you have the correct motor?
Did you get a new capacitor that matches the new motor?

Usually the brown and brown white go to the capacitor.

To hook up there is a wiring diagram on the side of the motor. They ALL have them.