Hi all. I am shaping a 5'5'' surfboard used for kiting; I'm using a500 core cell foam with S cloth and epoxy. Would those materials possess enough stiffness and strength or do I need to put a stringer in the board?

Depends on fibre weight and direction.

I'd imagine that you could go with out, most (pretty much all) EPS boards don't have stringer.

Hein probably has the answer, he's done a couple Divy and Airex boards with no stringers from what I've seen and it would be the same answer for A600.