Step 1: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrr} & & -c^2 \\ \color{red}{ - } & 5c^3 & \\ \hline \end{array} $$Step 2: Change ALL the signs in the second row.
$$ \begin{array}{lrr} & & -c^2 \\ \color{red}{ - } & -5c^3 & \\ \hline \end{array} $$Step 3: Combine like terms (add each column):
$$ \begin{array}{lrr} & & -c^2 \\ \color{red}{ - } & -5c^3 & \\ \hline & 5c^3 & -c^2 \end{array} $$