iPhone 5S No Service/Mobile Data Error

See this Apple article: If you see No Service or Searching on your iPhone or iPad

If you see No Service or Searching on your iPhone or iPad - Apple Support

Update Required

iPhone 5S is an outdated iPhone, can’t be update to a higher iOS.

iOS 12.5.5 is the latest iOS security update -> released September 23, 2021.

Hi - Assuming you are in USA:

As of March 1, 2022, AT&T is no longer offering the 3g technology that powered your phone. Other US carriers will follow suit; T-Mobile in July, Verizon in December. This was done at the request of the FCC. There is nothing that we or Apple can do.

Here is AT&T's notification→https://www.att.com/ecms/dam/att/consumer/help/pdf/Devices-Working-on-ATT-Network-After-3G-Goes-Away.pdf