Was hoping for some help adapting this circuit from +12V / -20V to +5V / -20V.

Are the two resistors on the +12V side the only components that will need to change?

 

Replace 1 MOhm resistor to a smaller resistor. Approximately 330 - 360 kohms. Use the LTspice.

 

Replace 1 MOhm resistor to a smaller resistor. Approximately 330 - 360 kohms. Use the LTspice.

Tried that, and instead of a steady output voltage I end up with this sawtooth wave:

 

Try larger filtering caps and/or larger inductor.