To get this solution you need the two Doom Books, which give you the first 4 holds in the right order.
Looking at the map of Skyrim these 4 holds are around another hold, the one where the mansion is placed. This hold is the 5th switch which needs to be pressed.
To get an overview about the holds, there is a colored map at a chimney 2nd floor, rear right side of the mansion.



Solution:
The combination is: Pale / Reach (Markarth) / Whiterun / Haafingar (Solitude), then Morthal.
Remember the sequence is not resetting (Dark Edition) if you use a wrong switch after a correct one, and survived the trap.
The shelf bellow the Morthal shield should open then and give you the Claw needed for the entry to the Lab.