High current, high frequency IC PWM switching with MOSFETs
20 Khz is very reasonable for MOSFET PWM.  Adding a MOSFET driver is important because even at this relatively low switching frequency, the gate capacitance will mean that your present circuit will switch slowly.  The IRF5305 in your circuit has a gate capacitance of 1200 pf and a reverse transfer capacitance of 250 pf, and you are driving the gate with a 10K impedance to turn it off.  A gate driver will provide low impedance in both directions (on and off) and result in reasonable switching times.

The IRF5305 has a gate threshold voltage of between -2 and -4 volts, but this only guarantees 250 uA, so you will want to drive the gate with at least -10 volts or so while staying well under the +/-20 volt maximum gate voltage.

Finally, if you are driving inductive loads, you must deal with the negative voltage spikes that will occur at turn-off with protection and possibly snubber circuitry.  This part will break down (acting like a zener diode) if these spikes exceed -55 V, and the MOSFET will have to absorb the energy, heating up and possibly failing.  A combination of a higher voltage MOSFET and snubber may be necessary.

Good luck!