You are right. Looking back I think the iPhone 5 is what had issues for some. I didn't think it was that wrong ago, but I guess it has been!
Slightly in correct. T-Mobile needed aws bands in the iPhone 5 (both upload and download) hspa plus 1700/2100.As far as I know, all 5S's have all the bands used by T-Mobile. The iPhone 5 lacked band 4 WCDMA/UMTS which was eventually added in an updated model.
Apple "tweaked" the A1428 version of the iPhone 5 in April 2013 to fully support T-Mobile.
https://www.macrumors.com/2013/03/2...a-tweaked-model-a1428-phone-with-aws-support/
So SOME iPhone 5 are compatible with T-Mobile network.