Will the Unlocked Apple Watch 5 work with my T-Mobile Carrier?

There is no such thing as an unlocked Apple Watch 5. If you purchase an Apple Watch 5 GPS+Cellular, it has to be the model designed for your location, and will only work on cellular with a carrier that supports cellular on the watch. There is no way to know where you are located, since you did not share that information. If you do not wish to activate the cellular portion of the Watch, it will still work with your iPhone present just like any GPS watch would. Apple Watch - Carriers - Apple

Apple Watches are not locked. If you buy from Apple, then it will work with any of the carriers. I'll assume you are U.S. based and will be buying in the U.S.

If you purchase a GPS only model, then the carrier does not get involved.

A GPS only model will do Everything the cellular model does as long as the iPhone is nearby. The cellular model just gets to leave the iPhone at home while you go for a walk, run, bike ride, etc...