iPhone 5S is an outdated iPhone, can’t be update to a higher iOS.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.
it keeps saying no internet connection
Try to optimize the range of the mobile network, see this Apple article:
If you see No Service or Searching on your iPhone or iPad
https://support.apple.com/en-us/HT201415
Check the Wi-Fi network, see the following Apple articles:
Connect to Wi-Fi on your iPhone, iPad, or iPod touch
https://support.apple.com/en-us/HT202639
If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network
https://support.apple.com/en-us/HT204051