Can I use my UK iPhone 5S in the USA? I have an iPhone 5S registered in the United Kingdom with a United Kingdom simcard and number from T-Mobile. I have moved to the USA permanently and cannot call or text any American numbers. I have been told this is because I need to get a US simcard and number. (Please correct if wrong)

I am considering Tracphone as a provider, and asked them if I can use their plan/sim/number in my physical phone from the UK. The answer was 


  If the phone is an unlocked GSM phone that must operate on 850 and 1900 MHz bands, you can use it.


(Bold emphasis mine). Does my UK-bought 5S fit those criteria?
Yes you can, according to https://support.apple.com/kb/sp685 all iphone 5s models can use GSM/EDGE on the 850 and 1900 bands, so you can make phone calls, text and use EDGE (know as 2G internet)

Cellular and Wireless:
Model A1533 (GSM)*: UMTS/HSPA+/DC-HSDPA (850, 900, 1700/2100, 1900, 2100 MHz); GSM/EDGE (850, 900, 1800, 1900 MHz); LTE (Bands 1, 2, 3, 4, 5, 8, 13, 17, 19, 20, 25)
Model A1533 (CDMA)*: CDMA EV-DO Rev. A and Rev. B (800, 1700/2100, 1900, 2100 MHz); UMTS/HSPA+/DC-HSDPA (850, 900, 1700/2100, 1900, 2100 MHz); GSM/EDGE (850, 900, 1800, 1900 MHz); LTE (Bands 1, 2, 3, 4, 5, 8, 13, 17, 19, 20, 25)
Model A1453*: CDMA EV-DO Rev. A and Rev. B (800, 1700/2100, 1900, 2100 MHz); UMTS/HSPA+/DC-HSDPA (850, 900, 1700/2100, 1900, 2100 MHz); GSM/EDGE (850, 900, 1800, 1900 MHz); LTE (Bands 1, 2, 3, 4, 5, 8, 13, 17, 18, 19, 20, 25, 26)
Model A1457*: UMTS/HSPA+/DC-HSDPA (850, 900, 1900, 2100 MHz); GSM/EDGE (850, 900, 1800, 1900 MHz); LTE (Bands 1, 2, 3, 5, 7, 8, 20)
Model A1530*: UMTS/HSPA+/DC-HSDPA (850, 900, 1900, 2100 MHz); GSM/EDGE (850, 900, 1800, 1900 MHz); FDD-LTE (Bands 1, 2, 3, 5, 7, 8, 20); TD-LTE (Bands 38, 39, 40)