Olympiad Geometry · Superchallenge problem

Triangles $ABC$ and $ADE$ are similar, with $A \leftrightarrow A$, $B \leftrightarrow D$ and $C \leftrightarrow E$, and both are labelled counterclockwise, so one is a rotated and scaled copy of the other about their common vertex $A$. Given $AB = 4$, $AC = 6$ and $BD = 5$, find $CE$.