To connect the wires: J-K-K-H-H-J

In the next room, interact with the man's head, then enter the code: 1258 on your num pad

In the last room, hit the 3rd button, then the 2nd, 1st, then 4th. They should have a faint diamond, circle, square, and triangle respectively.

Note: there is a glitch where after loading into the bonus level from a save, the last door won't open when the buttons are pressed. You need to load into level 5-4 and beat it to complete level 5-Bonus. Probably a little useful for segmented runs ;)