
Samsung Galaxy Tab3
The latest firmware for Samsung Galaxy Tab3 (GT-P5200) is P5200XXUBOH1 with Jelly(Android Bean), released on September 16, 2015 for 5 regions (CSC). Every official firmware build for GT-P5200, 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/P5200XXUBOH1
All 28 builds in our database run Android 4.4.2 (Jelly). The newest build, P5200XXUBOH1, was released on September 16, 2015. No new build has appeared for 135 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-P5200 runs Android 4.4.2 (Jelly): build P5200XXUBOH1, released on September 16, 2015.
The latest build for GT-P5200, P5200XXUBOH1, was released on September 16, 2015 (11 years ago).
GT-P5200 has had no new firmware for 135 months, so regular updates have most likely ended.
Yes, all firmware files for GT-P5200 are 100% official, original, and obtained directly from Samsung servers.
To flash GT-P5200, 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-P5200.