K1823 Potentiometer replacement?

I was reading the instructions for this kit, and it says: “Replace the trimmer with a potentiometer of the same rating if you want to use the circuit as a permanently adjustable power supply.”

What exactly does this mean? I obviously want to use this for a wide variety of voltage outputs, I have to replace the potentiometer that is with the kit? Is this potentiometer not good for adjusting voltage? Is it because it requires a screwdriver to change voltage? What would be a suitable replacement?

Yes, it is because it needs a screwdriver.
You can replace it by a potmeter with knob with the same specifications (i.e. same resistance).

I cannot seem to find 4.7k ones around here, would a 5k be fine?

Yes.