5. (3 points) Three circles with radii 1, 1, and \(2 \sqrt{\frac{13-6 \sqrt{3}}{13}}\) are arranged such that the triangle formed by their centers is equilateral with a side length of \(\sqrt{3}\). Find the radius of the circumcircle of the triangle, each vertex of which is the point of intersection of two of these circles, farthest from the center of the third circle.

Answer: \(4 \sqrt{3}-6\)