The MP5 controller should work in a MP4 motor as the MP4 and MP5 are both designed to work with vector controllers, but the MP4 and MP5 controllers are not compatible with the MPIII.
The different Hall sensor sockets do not use the same pin configuration, so the motor will not run until the Hall sensor wires are correctly configured.
If you have the small white socket, the wires should be connected as shown here:
But if you have the larger black socket, the wires may need to be connected as shown here:
I have tried to show the Hall connector wires more clearly in the attachment below.
Alan