  Let $X$ be a smooth quintic hypersurface in $\mathbb{P}^3$, let $C$ be a
smooth hyperplane section of $X$, and let $H=\mathcal{O}_X(C)$. In this paper,
we give a necessary and sufficient condition for the line bundle given by a
non-zero effective divisor on $X$ to be initialized and aCM with respect to
$H$.
