It is possible to root the device GT-5200 (3G+wifi)?
Don't know if you still need to know the answer.
I'll just write a short answer, so anybody reading this thread can find the right page:
Found this Tutorial via Google:
How to Root Galaxy Tab 3 10.1
This is the original Thread on XDA:
[RECOVERY][CWM][UNOFFICIAL] Clockworkmod Recovery [FINAL] and ROOT