1. The problem asks to write a compound inequality describing the graph segment between -5 and -4 on the number line. 2. The graph shows a thick magenta line segment from -5 to -4. 3. The endpoint at -5 is an open circle, meaning -5 is not included in the solution. 4. The endpoint at -4 is a closed circle, meaning -4 is included in the solution. 5. Therefore, the compound inequality is $-5 < x \leq -4$. 6. This means $x$ is greater than -5 but less than or equal to -4.