How to enable CTRL+4/5/6?
I had a similar issue of unresponsive Ctrl+3 and Ctrl+4 keystrokes using OS X 10.8.4 and found a solution that worked for me using information from this answer.


Open ~/Library/Preferences/com.apple.symbolichotkeys.plist (I used XCode).
Update keys for the shortcuts which are giving you trouble by switching enabled to NO. I switched 120 and 121, which represent Ctrl+3 and Ctrl+4. I am not sure about Ctrl+5 or Ctrl+6.
Restart your computer.


Hope this helps!