Answer
$\frac{10\sqrt3}{3}$
Work Step by Step
We first draw the perpendicular triangles. We then draw a vertical line from the circumcenter to the base of the isosceles triangle. This creates two 30-60-90 triangles, where the base of each triangle is 5. Using the lengths of 30-60-90 triangles, we see that the distance is:
$$ 2(\frac{5}{\sqrt3}) \\ = 2(\frac{5\sqrt3}{3} )\\ = \frac{10\sqrt3}{3}$$
