Where do you get your tap water from? If it's town or city water there is no way it's pH5. That would corrode their whole system so even if the feed water is 5 they will buff it up over 7 with calcium carbonate or something similar so it's slightly alkaline and won't rot the system out.
If it's from a well then it's possible but still very unlikely as almost all ground water is over pH7 naturally. River or lake , (surface water), water can be lower as it has little contact with with minerals that would raise the pH. Rain water is generally acidic and can be as low as pH5 if there's acid rain going on from pollutants like coal fired generating plants downwind.
Double check your testing procedure or maybe get a new kit of a different brand. pH pen is best but needs care and calibration to keep it working right.
Check with your water supplier and request a copy of their water analysis by email. Get the full report and not the dumbed down one they hand out to Joe Public. Should have the pH, ppm and a list of how much of what is in your water. Should be free too.