How to use MOSFET for load switch applications
In order to adequately turn the MOSFET on there needs to be "several" volts between gate and source. If you apply 5 volts to the gate and the gate-source threshold voltage is exceeded you will begin to see some voltage at the source but you won't see 20 volts because this is a source follower circuit.

A better circuit is to put your 22 kohm resistor in series with the drain up to 20 volts and have the source connected to ground/0 volts. This is called a common-source configuration and you will be able to switch virtually the full rail across the load.

Alternatively, if you need a ground connected load you would use a PMOS FET: -



R3 stops the full 20 volts being applied across GS of the PMOS FET because that might otherwise be close to the limit for a typical device.