Facebook not installed

Correction - you can update a 5S to iOS12.5.5. Once you have done that you can install Facebook. If you are getting the message that your iOS is up to date then you have a 5 not a 5S and a 5 cannot be updated further.

The Facebook app requires iOS12.4 at least. You cannot run it on a 5S.

You don't have a 5s, you have a 5.