too many people are saying it will but apparently Apple and T-mobile say it won't...
"Though Apple's spec sheet for the current AT&T iPhone 5 says that it has support for T-Mobile compatible LTE (Band 4, AWS), the official stance given to The Verge by both Apple and T-Mobile is that LTE is not supported with the current iPhone 5. While the iPhone 5 sings on AT&T's LTE network, it won't even connect to T-Mobile's. "
link to the article: http://www.theverge.com/2013/3/26/4150856/bringing-your-iphone-to-t-mobile-better-think-twice
"Though Apple's spec sheet for the current AT&T iPhone 5 says that it has support for T-Mobile compatible LTE (Band 4, AWS), the official stance given to The Verge by both Apple and T-Mobile is that LTE is not supported with the current iPhone 5. While the iPhone 5 sings on AT&T's LTE network, it won't even connect to T-Mobile's. "
link to the article: http://www.theverge.com/2013/3/26/4150856/bringing-your-iphone-to-t-mobile-better-think-twice