Let $\mathcal{A}$ be a set of connected graphs. A graph $G$ has an $\mathcal{A}$-factor if $G$ has a spanning subgraph $H$ such that each component of $H$ is isomorphic to one of the members in $\mathcal{A}$. In this paper, we give a necessary and sufficient condition for the existence of $P_5$-factors in line graphs of trees. Then we present an algorithm to search for a $P_5$-factor in the line graph of a tree.