LTE 4 / 13
WCDMA 1 / 2 / 5 / 8
CDMA 850 / 1900
GSM 850 / 900 / 1800 / 1900
T-Mobile is a GSM network for which Verizon is CDMA. T-Mobile does not have use for CDMA radios. So, in turn, the CDMA Verizon S5 will be of little to no use on T-Mobile's GSM network.
But the phones are THE SAME under the covers -- the particular radios just get activated as required by the service being connected to. MUCH simpler (read that cost-effective) for the manufacturer when they sell the units to all of the carriers.
I see in various forums lots of happy users of Verizon S5 phones that have moved over to T-Mobile accounts. In this case, since the person already has the S5 and just wants to activate it on T-Mobile, they can just try it and see. Very little risk, since no money (except activation charge) is necessary.....
Yeah, go ahead and give it a try.
Here's the thing. They ARE NOT the same under the covers. That's why there is a difference. Some can use PORTIONS of the phone on other carriers. They cannot use it 100%. Also, hotspot most likely won't work. Coverage will be reduced. Speeds will not be as expected. I'm not sure how else to explain this to you. If all versions of of the same model name were all the same save the model number, then people would be taking the same phone with them all over the place to all carriers for new customer deals. The deal is, unlocked to run on other carriers that are COMPATIBLE ...not a guarantee to work just because "unlocked" is used in a description.
OP, basically, give it a try and see if T-Mobile will allow it to be brought to their network. It is their prerogative to allow it to be used or attempted to be used on their network. Law might require a phone NOT be locked to ONE carrier, but law does NOT mandate that any phone can be used on every carrier, only the carriers who allow on their network and phones compatible with their network.
That's a far cry from "will not work", which was the original assertion. Indeed in this case a better answer would be "should MOSTlLY work, but your millage may vary."
Let's get real here. Are you going to want to go through all that headache to TRY to get a phone to work on an incompatible carrier? Really? You want no calls, dropped calls, slow data, no data, issues getting a T-Mobile rep online or in a store to activate it, to find out the IMEI/ESN is not in their system and try to convince them, after being told NO, to still allow you to activate anyway? This isn't a matter of CAN, this is a matter of SHOULD.
You left out "you might step into an electrified puddle while you're talking on it....."
NOW you're getting into Verizon-PR territory.
Look, the guy isn't trying to jump ship, he's passing it on to a relative who's already on T-Mobile. No need to go through the horror-stories of what COULD happen in rare circumstances that are used to dissuade a ship-jumper. When it's a free phone replacing an old dog phone, a few foibles are perfectly acceptable to many people.
The following is what I found on phonearena:
There are some differences. You may have better luck trying to sell it on Swappa.com and purchasing one for T-Mobile from the same place. Sometimes you can simply trade.
This doesn't get into which of those differences are commonly used where.... From what I've heard, the ones that are shared are the most commonly used ones, so these differences would be of little effect for most users....
The net is still "should work pretty well, but your mileage may vary".
Maybe it is just me, but I prefer "will work well" as in a T-Mobile device. I think the "net" is for best results, sell it and get one designed for the carrier with the proceeds.