Now you haven't given us the exact model of which LED switch you are using but the 5 pins probably look something like this:
simulate this circuit – Schematic created using CircuitLab
By the looks of the image, 1 and 5 is where the LED connects where 5 would be the anode (positive connection) and 1 would be the cathode (negative) connection. This is the reason why the LED stays on.
This leaves us with 2, 3 and 4 for the switch. There would be a common, NC and NO. Get a continuity meter or a simple open circuit with an LED (or buzzer) like the following (you could even use the LED in the switch):
simulate this circuit
And try which one of pins 2,3 or 4 are shorted together (making the LED light up or the continuity meter beep) while NOT pressing the push button. Then hold the push button down and try again. The pin that is used in the two experiments is the common, while the others are when it's push and when it's not pushed (NO and NC).
If your switch is good enough to handle the current of the motor (which must be pretty high), then do a circuit like this:
simulate this circuit
This means the LED will always be on and the button just turns the motor on and off.
If your switch can't handle motor current, then you may need a relay that can handle the high currents.
simulate this circuit