Samsung Galaxy Tab 3 10.1 LTE (GT-P5220) Firmware Overview
What is the latest GT-P5220 firmware?
P5220XXUBOA2, released March 13, 2015 for region NEE with Android 4.4.2. The archive holds 2 official builds for this region.
Is the Samsung Galaxy Tab 3 10.1 LTE still getting updates?
Most likely not: there has been no new firmware since March 2015, so Android 4.4.2 is the last version this model got. The final builds below are still the best choice for a clean reinstall.
GT-P5220 firmware for region NEE
How to Flash GT-P5220 Firmware
Put the Samsung Galaxy Tab 3 10.1 LTE into Download Mode, load the BL, AP, CP and CSC files into Odin on a Windows PC and press Start. Use HOME_CSC to keep your data, CSC for a full wipe.