Let ​ Then P can be expressed in the form a^(b/c) where a,b, and c are positive integers. Find the smallest possible value of a+b+c.

Let \(P = 5^{1/5} \cdot 25^{1/25} \cdot 125^{1/125} \cdot 625^{1/625} \dots\)
Then P can be expressed in the form a^(b/c) where a,b, and c are positive integers. Find the smallest possible value of a+b+c.