Decompositions of highly connected graphs into paths of length five

We study the decomposition conjecture posed by Barát and Thomassen (2006), which states that, for each tree T, there exists a natural number kT such that, if G is a kT-edge-connected graph and |E(T)| divides |E(G)|, then G admits a partition of its edge set into classes each of which induces a copy of T. In a series of papers, starting in 2008, Thomassen has verified this conjecture for stars, some bistars, paths of length 3, and paths whose length is a power of 2. In this paper we verify this conjecture for paths of length 5.