  We study the Decomposition Conjecture posed by Bar\'at and Thomassen (2006),
which states that for every tree $T$ there exists a natural number $k_T$ such
that, if $G$ is a $k_T$-edge-connected graph and $|E(T)|$ divides $|E(G)|$,
then $G$ admits a decomposition into copies of $T$. In a series of papers,
Thomassen verified this conjecture for stars, some bistars, paths of length
$3$, and paths whose length is a power of $2$. We verify the Decomposition
Conjecture for paths of length $5$.
