A circle is inscribed in a regular triangle, the radius of which is 5. Then what is the median of this triangle.

A triangle in which all sides are equal is called a regular (or equilateral) triangle.
Each of the heights h of a regular triangle is also its median m and bisector b: h = m = b.
For any triangle: 2 * S = r * (a + b + c), where a, b, c are the lengths of the sides, S is the area, r is the radius of the circle inscribed in the triangle.
For a regular triangle: 2 * S = 3 * a * r; moreover, S = a * h / 2.
We have: a * h = 3 * a * r, whence h = 3 * r = 3 * 5 = 15, that is, m = 15.
Answer: 15.