Answer
See graph.
$(-\infty,\infty)$, $[2,8]$.
Work Step by Step
Step 1. See graph for $y=5-3sin(2x)$ with key points or transform from $y=sin(x)$ (shrink horizontally by a factor of $2$, stretch vertically by a factor of 3, reflect across the x-axis, then shift 5 units up.)
Step 2. Based on the graph, we can determine the domain as $(-\infty,\infty)$ range as $[2,8]$.
