jmc

We first draw a diagram: This is a bit hard to comprehend, so let us add $\overline{AC}.$ Now we can see that $\overline{AB}$ and $\overline{CD}$ are altitudes to the triangle $ACE.$

That means we can come up with two different ways to find the area of $ACE.$ Setting them equal, we have: $$\begin{array}{rl}\frac{1}{2}\cdot AB\cdot CE& =\frac{1}{2}\cdot CD\cdot AE\\ AB\cdot CE& =CD\cdot AE\\ 4\cdot CE& =8\cdot 5\\ CE& =\boxed{10}.\end{array}$$