Let $u(x_1,...,x_n)$ be a word, $k\in \mathbb{N}$. We say that $u$ is $k$-avoidable if there exists an infinite word in $k$ letters $\{a_1,...,a_k\}$ which does not contain values of $u$ (i.e. words of the form $u(v_1,...,v_n)$, $v_i\in \{a_1,...,a_k\}^+$ as a subword. For example $x^3$ is 2-avoidable and $x^2$ is 3-avoidable but not 2-avoidable because two infinite words constructed by Thue and Morse avoid $x^2$ and $x^3$. All avoidable words have been described by Bean-Ehrenfeucht-McNulty and Zimin (see <a href="http://www.math.sc.edu/~mcnulty/talks/victoria.pdf">these</a> slides, for example.

* Is there an example of a $5$-avoidable but not $4$-avoidable word? 

Ronald Clark in his PhD thesis claimed that $$abubawacxbcycdazdcd$$ is such a word. But his thesis (UCLA, 2001) does not seem to be published. What is the status of that result?