Her brand new iPhone5, purchased earlier this year and which would presumably have a brand new battery, has slowed right down.
Her "new" iPhone 5 is likely a refurb with an old battery. She can take it to Apple and they can put it on a gizmo that will show the number of charge/discharge cycles on the battery (the LiIon batteries have a tiny on-board computer that records this) and the total battery charge life left.
