Can we find the sum of series, $$\frac{1}{5} + \frac{1}{2\cdot 5^2}+ \frac{1}{3\cdot 5^3}+\dots $$.
If this 2,3 were in numerator , then this is AGP, which we know how to solve, by multilying by common ratio and shifting one term to left. But same approach is not working here.
As suggested in comments, the Maclaurin series for $-\log(1-x)$ is $$\sum_{k=1}^\infty\frac{x^k}k=x+\frac{x^2}2+\frac{x^3}3+\dots\qquad|x|<1$$ Now take $x=\frac15$.