Step 1: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrr} & & m & 5 \\ \color{blue}{ + } & m^2 & 4m & -8 \\ \hline \end{array} $$Step 2: Combine like terms (add each column):
$$ \begin{array}{lrrr} & & m & 5 \\ \color{blue}{ + } & m^2 & 4m & -8 \\ \hline & m^2 & 5m & -3 \end{array} $$