  In this paper I consider a quintic surface in $\pp^3$, general in the sense
of Noether-Lefschetz theory. The vector bundles of rank 2 on this surface which
are $\mu$-stable with respect to the hyperplane section and have $c_1 = K$, the
canonical class of the surface and fixed $c_2$, are parametrized by a moduli
space. This space is known to be irreducible for large $c_2$ (work of K.G.
O'Grady). I give an explicit bound, namely $c_2 \geq 16$.
