Answer
See graph.
$(-\infty,\infty)$, $[-\frac{5}{3},\frac{5}{3}]$.
Work Step by Step
Step 1. See graph for $y=\frac{5}{3}cos(-\frac{2\pi}{3}x)$ with key points or transform from $y=sin(x)$ (shrink horizontally by a factor of $\frac{3}{2\pi}$, reflect across the y-axis, then stretch vertically by a factor of $\frac{5}{3}$.)
Step 2. Based on the graph, we can determine the domain as $(-\infty,\infty)$ range as $[-\frac{5}{3},\frac{5}{3}]$.