The C5 has smoother highs and more bass. That can be good or bad, depending on your style. The 59 is somewhat transparent, but edgy. It's very pure and I love the attitude and punch that it has. The C5 is a bit smoother.
If a 59 was a nicely EQ'd and pleasant sounding stereo, the C-5 would be like pushing the bass boost button. That's what it sounds like when you alternate between two Pauls....a 59 in one, and C-5 in the other.