Samsung Galaxy Tab 3 10.1 LTE (GT-P5220) Firmware Overview
What is the latest GT-P5220 firmware?
P5220XXUBPA1, released January 16, 2016 for region PHN 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 January 2016, 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 PHN
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.