# Joining in the path madness

Brilli the ant stands at a vertex, $$A$$, of an icosahedron. After every minute, he travels to one of the five adjacent vertices, along an edge, with equal probability. After $$10$$ minutes, having traveled $$10$$ times, the probability that he is back at vertex $$A$$ can be expressed as $$\frac{m}{5^{10}}$$. Find the value of $$m$$

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