
Samsung Galaxy Tab3
The latest firmware for Samsung Galaxy Tab3 (GT-P5210) is P5210XXUBPF1 with Android 4.4.2 (KitKat), released on June 2, 2016 for 2 regions (CSC). Every official firmware build for GT-P5210, newest first: one row per build with all regions (CSC) that received it.
Each firmware build has its own page at https://samfirm.shop/build/{PDA}, where {PDA} is the build number from the list above. Example: https://samfirm.shop/build/P5210XXUBPF1
All 33 builds in our database run Android 4.4.2 (KitKat). The newest build, P5210XXUBPF1, was released on June 2, 2016. No new build has appeared for 126 months, so regular updates for this model have most likely ended.

GT-P6810

GT-P6211

GT-P6210

GT-P6200

GT-P1010

GT-P1000N

GT-P1000M

GT-P7320T
The newest firmware for GT-P5210 runs Android 4.4.2 (KitKat): build P5210XXUBPF1, released on June 2, 2016.
The latest build for GT-P5210, P5210XXUBPF1, was released on June 2, 2016 (10 years ago).
GT-P5210 has had no new firmware for 126 months, so regular updates have most likely ended.
Yes, all firmware files for GT-P5210 are 100% official, original, and obtained directly from Samsung servers.
To flash GT-P5210, you need to download the appropriate firmware, put your device into Download Mode, and use the Odin tool to load the BL, AP, CP, and CSC files.
Downgrading is only possible if the bootloader version (binary bit) of the old firmware matches the current one. Always check the binary version before flashing GT-P5210.