Step 1: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrr} & 5m^3 & 3m & 5 \\ \color{blue}{ + } & 18m^3 & & 10 \\ \hline \end{array} $$Step 2: Combine like terms (add each column):
$$ \begin{array}{lrrr} & 5m^3 & 3m & 5 \\ \color{blue}{ + } & 18m^3 & & 10 \\ \hline & 23m^3 & 3m & 15 \end{array} $$