  We study semistable sheaves of rank $2$ with Chern classes $c_1=0$, $c_2=2$
and $c_3=0$ on the Fano 3-fold $V_5$ of Picard number $1$, degree $5$ and index
$2$. We show that the moduli space of such sheaves has a component that is
isomorphic to $\mathbb{P}^5$ by identifying it with the moduli space of
semistable quiver representations. This provides a natural smooth
compactification of the moduli space of minimal instantons, as well as Ulrich
bundles of rank $2$ on $V_5$.
