5. (3 points) In a regular triangular pyramid (not a regular tetrahedron), the area of the base is half the area of a lateral face. The height of the pyramid is 70 cm.

Consider the following (infinite) sequence of spheres. Let \( S_{1} \) be the inscribed sphere of this pyramid. Then \( S_{2} \) is the sphere that is tangent to the lateral faces of the pyramid and to the sphere \( S_{1} \); \( S_{3} \) is the sphere that is tangent to the lateral faces of the pyramid and to the sphere \( S_{2} \), not equal to \( S_{1} \), and so on; \( S_{n+1} \) is the sphere that is tangent to the lateral faces of the pyramid and to the sphere \( S_{n} \), not equal to \( S_{n-1} \).

Find the total volume of all these spheres.
Answer: $\frac{686}{327} \pi$ dm $^{3}$.