Will an unlocked iphone 5 work with any nano SIM card?

My friend is selling me her iphone 5. It's factory unlocked from verison, but she was on tmoblie service. I use straight talk and you can bring your own phone, you just have to buy the nano sim. I bought a tmobile compatible nano sim, assuming since she was on tmoblie service, she bought it from them. Should this be a problem or is this okay?

TMobile iPhones will work with any Nano Sim chip. I use one in Costa Rica.

Hence the unlock.

It won't be a problem. Just get it on.