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