$$5 + 5 ^ { 2 } + 5 ^ { 3 } + - - - - - + 5 ^ { n } = 5 ( 5 ^ { n - 1 } )$$
$n=\frac{2\pi n_{1}i}{\ln(5)}+\log_{5}\left(\frac{155}{2}\right)$
$n_{1}\in \mathrm{Z}$
$n=\log_{5}\left(\frac{155}{2}\right)\approx 2.702979657$
