I was in a similar position as you. I'm a hair under 5'11" and when I got back in to road bikes, I had picked up a nice 1984 Centurion Elite RS with a 62cm frame.

No matter what I did to adjust things I was never completely comfortable on the bike. Any rides longer than 10 miles or so would result in (pick one or more) neck/shoulder/back/hip/genital soreness.

I built up a 58cm Trek Elance 310 and I'm MUCH more comfortable. I ended up at the 58cm size by using the fit calculator several people already posted.

Welcome aboard, good luck finding a frame to fit you, and keep us posted!