Answer
False
Work Step by Step
To determine if a proportion is true, we have to find if the cross products are equal.
The cross products of $\frac{a}{b}=\frac{c}{d}$ are $a \cdot d$ and $b \cdot c$.
$5\frac{5}{8} = \frac{45}{8}, 4\frac{1}{2} = \frac{9}{2}, 1\frac{1}{5} = \frac{6}{5}$
$\frac{45}{8}*\frac{6}{5} = \frac{27}{4}, \frac{9}{2}*\frac{5}{3} = \frac{15}{2}, \frac{27}{4} \neq \frac{15}{2} \rightarrow$ false