Sum includes powers of 5

Algebra Level pending

Compute :

\[ \frac{1}{5}+ \frac {1}{5^2} + \frac{2}{5^3}+ \frac{3}{5^4}+ \frac{5}{5^5}+ ... = \frac{A}{B}\]

Each numerator is the sum of the two preceding numerators, and each denominator is \(5\) times the preceding one.

What is \(A+B =?\) (where \(A\) and \(B\) are coprime positive integers).

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