AT&T iPhone 5 on T-Mobile network?

Will an unlocked iPhone 5 from ATT get 4G or LTE once an Tmobile sim has been put in?

I think you can only use 3G, no 4G if the phone is not a T-Mobile phone.

May or may not, most likely not for now. T-Mobile is setting up iPhone compatible 4G/LTE currently. Their 3G signals are different than what the iPhone uses, so you'd be relegated to 2G, assuming you are not in one of the areas that already received it.