Find the sum of the series $5+55+555+..........$ upto $n$ terms.

Question

$\begin{array}{1 1}\large\frac{5}{81}\big[10^{n+1}-10+9n\big] \\ \large\frac{5}{81}\big[10^{n+1}-10-n\big] \\ \large\frac{5}{81}\big[10^{n+1}-10-9n\big]\large\frac{5}{81}\big[10^{n}-10-9n\big] \\ \end{array}$