Can I have my iPhone 5 unlocked from t-mobile for free?

If not, what is the next cheapest option?

No they will definitely not unlock your phone even if you offered to pay, i would suggest you google for phone unlocking services in your local area.
I don't know if you have a CEX store in your local area? But if you do? Then they have a phone unlocking service. But do be warned though the iphone normally costs quite a bit to get unlocked.

Most of the time you can go to the company store your phone is from and they will fix any minor problems For free. I'm not sure but the easiest way to find out is to ask call and ask them or go to the nearst store and explain your problem.

Here's a website you can find your local T moblie store and call them and ask them:

http://m.t-mobile.com/store?cm_mmc_o=VzbpjmwzygtCjC-czywEwllCjCVzbpjmwzygtCjCVzbpjmwzygt

If you don't have another phone to call on your best bet is to still use the website and find a store close to you that you can go in and explain your situation to. Hope i helped and good luck!

If its on contract then yes they should be free they have no reason not to as your still a T mobile customer and still in contract. If its pay as you go then they will charge you

I don't think you have a free option to do that