  The reconfiguration graph of the $k$-colorings of a graph $G$, denoted
$R_{k}(G)$, is the graph whose vertices are the $k$-colorings of $G$ and two
colorings are adjacent in $R_{k}(G)$ if they differ in color on exactly one
vertex. A graph $G$ is said to be recolorable if $R_{\ell}(G)$ is connected for
all $\ell \geq \chi(G)$+1. We use the modular decomposition of several graph
classes to prove that the graphs in the class are recolorable. In particular,
we prove that every ($P_5$, diamond)-free graph, every ($P_5$, house,
bull)-free graph, and every ($P_5$, $C_5$, co-fork)-free graph is recolorable.
