Can an iphone 5 use t-mobile without a factory unlock?

And what does an Rsim unlock mean?

Hi, it depends on whether the iPhone 5 was purchased from T-Mobile or not. If not, then you would have to unlock it (factory unlock) or use a SIM adapter such as R-Sim. Simple as that!

Only if was a T-Mobile iPhone 5 to begin with.

RSIM is a special SIM to unlock iPhones. Never used one personally though.

HI you can use iphone 5 with t-mobile only if it is unlocked one.Else if the iphone 5 is locked to some other network provider then until you unlock it you can't freely use it with any GSM sim. You can easily unlock the iphone 5 using http://www.wickedunlock.com/apple-iphone-5/rs1wp9/ here they are providing remote unlocking service to unlock all model iphone from network lock. You first check that whether the service is available for your country and network provider. If yes then pay for it and unlock your iphone.