anyway, here's the solution:

$\displaystyle \ln (5 - x) = \ln 5 \left( 1 - \frac x5 \right)$

$\displaystyle = \ln 5 + \ln \left( 1 - \frac x5 \right)$

$\displaystyle = \ln 5 - \frac 15 \int \frac 1{1 - \frac x5}~dx$

$\displaystyle = \ln 5 - \frac 15 \int \sum_{n = 0}^\infty \left( \frac x5 \right)^n~dx$

$\displaystyle = \ln 5 - \frac 15 \sum_{n = 0}^\infty \int \left( \frac x5 \right)^n~dx$

$\displaystyle = \ln 5 - \frac 15 \sum_{n = 0}^\infty \frac {5\left( \frac x5 \right)^{n+1}}{n + 1}$

$\displaystyle = \ln 5 - \sum_{n = 1}^\infty \frac {\left( \frac x5 \right)^n}n$

$\displaystyle = \ln 5 - \sum_{n = 1}^\infty \frac {x^n}{5^nn}$

Now you can go to bed