1. The problem asks to write a compound inequality describing the graph shown on the number line. 2. The graph shows an open circle at $-5$ and a closed circle at $-4$, with a solid line connecting these points. 3. An open circle means the endpoint is not included, so $x$ is strictly greater than $-5$. 4. A closed circle means the endpoint is included, so $x$ is less than or equal to $-4$. 5. Combining these, the compound inequality is: $$-5 < x \leq -4$$ 6. This inequality means $x$ is any number greater than $-5$ but less than or equal to $-4$. Final answer: $$-5 < x \leq -4$$