Chosen Solution
your iphone 5s could not be activated because the activation server cannot be reached. try connecting your iphone to itunes to activate it, or try again in a couple of minutes itunes not connectad
Try using 3UTools and see if you can get it activated through there. Also check if IMEI is being displayed there. If IMEI is shown as N/A then the phone has a board issue relating to the baseband circuit which can only be fixed via micro-soldering / board-level repair. Personally I don’t think it’s worth fixing if the phone has this issue.