That is OK to do, now just let up on the pinkie, and slide the index down a couple frets and you are there--

You need to do this because there isn't a lot of point in playing a C chord up there unless you can move effortlessly from playing bass lines, and shuffle solos using extensions--In other words, that index finger holds the C triad(G-C-E), across three strings on the fifth fret and the other fingers bounce around playing bass and lead lines--