5. (8 points) Given an isosceles right triangle with a leg of 10. An infinite number of equilateral triangles are inscribed in it as shown in the figure: the vertices lie on the hypotenuse, and the bases are sequentially laid out on one of the legs starting from the right angle vertex. Find the sum of the areas of the equilateral triangles.
Answer: 25 .

![](https://cdn.mathpix.com/cropped/2024_05_06_9097957c4e1b0af2d762g-1.jpg?height=371&width=374&top_left_y=1548&top_left_x=1435)