  Motivated by the problem of reconstructing evolutionary history, Nishimura et
al. defined $k$-leaf powers as the class of graphs $G=(V,E)$ which has a
$k$-leaf root $T$, i.e., $T$ is a tree such that the vertices of $G$ are
exactly the leaves of $T$ and two vertices in $V$ are adjacent in $G$ if and
only if their distance in $T$ is at most $k$. It is known that leaf powers are
chordal graphs. Brandst\"adt and Le proved that every $k$-leaf power is a
$(k+2)$-leaf power and every 3-leaf power is a $k$-leaf power for $k\geq 3$.
They asked whether a $k$-leaf power is also a $(k+1)$-leaf power for any $k\geq
4$. Fellows et al. gave an example of a 4-leaf power which is not a 5-leaf
power. It is interesting to find all the graphs which have both 4-leaf roots
and 5-leaf roots. In this paper, we prove that, if $G$ is a 4-leaf power with
$L(G)\neq \emptyset$, then $G$ is also a 5-leaf power, where $L(G)$ denotes the
set of leaves of $G$.
