I'm not sure about the weakly conducting part but a strong acid can still produce a pH of 5 in water depending on how much water it is added to...that has nothing to do with the strength of the acid. I too am confused when it says that it is "much less than the concentration of the unknown compound itself" when nowhere in the passage do we know this information. I guess I was overthinking it and should've accepted that most times something with a pH of 5 will be a weak acid and the AAMC is looking for general knowledge like that not necessarily anything more specific, but it bugs me that it could technically be a strong acid.