Timp. You go 5 miles in a straight line and you go from 4600 ft to 11752 so 7152 ft increase. Murchison, NC is also about 5 miles from the peak of Mount Mitchell. Murchison is at 2930 ft and the peak of Mitchell is at 6684 so an increase of 3754 ft.
The Prominence listed for Timp is 5296 ft while Mitchell is at 6089. Something seems off about that.