Hey T-Mo. Nice job on all that Uncarrier stuff - it's really impressive the way you're strong-arming the rest of the American carriers into some more modern approaches to selling service. But you've still got at least one thing on common with your erstwhile Uncompetitors - a generally lousy record of updating everything except flagship smartphones. Case in point: the 8.4-inch Galaxy Tab S, which was an impressive (and expensive) tablet released last year, is just now getting its Android 5.0 update from 4.4. Boo.
It's actually not quite as bad as it looks. To our knowledge Samsung hasn't released any 5.1 builds for the Tab S family, so this 5.0.2 build is the latest official software from the manufacturer. (Which still kind of sucks, since 6.0 is right around the corner. If it's any consolation, the new Tab S2 models also run Android 5.0.) But that still leaves T-Mobile three months behind its competitors, which released Android 5.0.2 for their versions of the Galaxy Tab S 8.4 back in June. It's even odder considering that T-Mobile updated the larger Tab S 10.5 in May along with other carriers. The support page says the update actually began on May 18th, but this appears to be the first day it's actually changed.
According to T-Mobile's support page, the software bump is the only thing that's different in the T807TUVU1BOE1 OTA. It's still a massive 1.1GB update, so you may need to clear some space in order to make room. You can check your Settings menu for an OTA alert or use Samsung's Kies software to flash it manually. As always, root-level modifications may cause flashing to fail.