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