Step 1: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrrr} & 4x^5 & & -7x & 7 \\ \color{blue}{ + } & & 5x^4 & 8x & -2 \\ \hline \end{array} $$Step 2: Combine like terms (add each column):
$$ \begin{array}{lrrrr} & 4x^5 & & -7x & 7 \\ \color{blue}{ + } & & 5x^4 & 8x & -2 \\ \hline & 4x^5 & 5x^4 & x & 5 \end{array} $$