Manitou Reservoir Trail Intersection and 7.8 Mile Sign
By my calculations it's only 6.75 miles to the summit from this sign, however that's not the real issue anyway. You are at about 9,450 feet elevation at this sign. Still another 4,665 feet to gain in elevation on your way to the summit.
Another 1/4 mile down the trail from the intersection you'll reach "the cut". A place where the trail cuts through some rocks and you get a beautiful unimpeded view of Pikes Peak. The rocks here make great seats for a short break to enjoy the view.