Set the screen saver to 20 minutes I set 20 minutes in System Preferences -> Desktop &amp; Screen Saver, however the screen saver starts after 5 minutes. I tried to log out and restart the mac with no success.

I should say that after restarting I can see 5 minutes again. So it looks like the settings were not saved.
Check the date for the file:
com.apple.screensaver.50A10F0D-581E-5D09-8966-646EE8532C5B.plist in Libary

after you made the time change, it should show the latest date/time.

If not, delete the file.