Registered: Apr 2010
Distribution: Debian, Ubuntu, Fedora, RedHat, DSL, Puppy, CentOS, Knoppix, Mint-DE, Sparky, Vsido, tinycore
First, you are misunderstanding what the key sequence does. Ctrl-Alt-F3 does NOT put you in init mode 3, it only opens the TTY3 console. CTRL-ALT-F1 would open the first console. X-Windows and your desktop or gui login page are still running (as are all of the other configured consoles), you just happen not to be looking at (displaying) them at the current time.
How many consoles are available, and thus how you get back to your GUI desktop, is configurable. Not all distributions configure the same by default. I have NEVER seen one that would put the GUI on console 5, though that would not be an unreasonable setup. I would try 6, 7, and 8: I am pretty sure you will find it at one of those. I have once found it on 11, but only once, and that configuration may have been 'adjusted' from the default.