The following is the Maclaurin series expansion of a function $(1+5x{)}^p,$ where $p$ is some real number:

$(1+5x{)}^p={\displaystyle \underset{n=0}{\overset{}{}}}{c}_n{x}^n=1+c_{1}x+c_2{x}^2+$dots

Suppose that $c_0=1($as already indicated above$)$ and $c_1=-0\mathrm{.}5.$ Find $p.$

Answer: $p=$

Now find $c_2.$

Answer: $c_2=$