RNP5, AIUI, refers to nav capability. It doesn't have any relationship to the actual equipment. Meeting RNP5 just means the device meets RNP5. It says nothing about the device itself, and most importantly, it does not imply that the device will only just meet it.
GPS is either working (and accurate to a few metres 99% of the time, and a few more the rest of the time) or it isn't (no reception, device has failed, etc).
I would bet that RNP5 goes back to inertial derived navigation, where an error of a mile or two is entirely plausible. INS uses DME/DME to keep itself reasonably accurate but often it won't have DME reception (e.g. over large swathes of France).
KNS80 and similar old RNAV solutions (VOR shifting) also comes to mind as likely applicable to this.