If that is an N channel FET then it will not work. Ths is because to turn it on you have to have a 5V difference between source and gate. As the source is connected to the LEDs then it is not stating at zero volts but the forward voltage drop of the LED plus what is dropped across the resistor.
You will not get more than 4.3V on the transistor's emitter as well.
Yo need a P type FET and base resistors and to put the LED and resistor in the collector of the transistor and not the emitter.
However when you have done all that you will still have trouble because the PWM signals will beat with each other, some work at diffrent frequencies so they will not add up like you hope they will.