What kind of motor is this?
It will be a Brushless DC motor, presumably with Hall sensors (the twisted cable).

Hopefully that should point you in the right direction in looking for a drive solution - there are many brushless DC drivers out there - sometimes called ESC's. But essentially they comprise of three half-bridges, one driving each phase. The Hall sensors feed back the rotor position to allow for correct timing when commutating the motor (switching phases digitally) without needing to resort to BEMF to determine rotor position which tends to be more tricky to do.

EDIT:

As Nick rightly points out I forgot about power when I was counting wires for the sensors. The twisted cables are probably some for of speed feedback. In this case you would need a driver which is designed to run BLDC motors which performs the commutation based on EMF from the motors.