  In this paper we continue our study of the moduli space of stable bundles of
rank two and degree 1 on a very general quintic surface. The goal in this paper
is to understand the irreducible components of the moduli space in the first
case in the "good" range, which is $c_2=10$. We show that there is a single
irreducible component of bundles which have seminatural cohomology, and
conjecture that this is the only component for all stable bundles.
