Answer
$-\displaystyle \frac{1}{4}x^{4}-\frac{7}{15}x^{3}-0.3$
Work Step by Step
$ \begin{array}{rrrrrr}
& \frac{1}{4}x^{4} & -\frac{2}{3}x^{3} & -5 & \\
+( & -\frac{1}{2}x^{4} & +\frac{1}{5}x^{3} & +4.7 & )\\
\hline & & & & \\
= & (\frac{1}{4}-\frac{1}{2})x^{4} & +(-\frac{2}{3}+\frac{1}{5})x^{3} & +(-5+4.7) & \\
& & & & \\
= & \frac{1-2}{4}x^{4} & +\frac{-10+3}{15}x^{3} & -0.3 & \\
& & & & \\
= & -\frac{1}{4}x^{4} & -\frac{7}{15}x^{3} & -0.3 &
\end{array} $