The Simplex 5 button safe lock is a very common lock for smaller pistol safes. It can be found on Viking, Fort Knox, Stealth safes and more.

It is also a common lock from commercial levers, being very popular since the 1970s.

To change the code of the Simplex lock: enter the current code, push the reset button, clear the lock by turning the knob to the left, enter the new code, clear the lock again.
To change a keyless simplex door lock code, the steps are the same except you clear the lock by pushing the lever down.

That's it.