5-Abelian cubes are avoidable on binary alphabets

A k-abelian cube is a word uvw, where the factors u, v, and w are either pairwise equal, or have the same multiplicities for every one of their factors of length at most k. Previously it has been shown that k-abelian cubes are avoidable over a binary alphabet for k >= 8. Here it is proved that this holds for k >= 5.