1. **State the problem:** We need to find the two double inequalities that define the shaded rectangular region on the coordinate plane. 2. **Identify the boundaries:** The shaded region extends horizontally from $x = -2$ to $x = 2$ and vertically from $y = 2$ to $y = 5$. 3. **Write the inequalities:** Since the region includes the boundary lines, we use $\leq$ (less than or equal to) for both variables. The inequalities are: $$-2 \leq x \leq 2$$ $$2 \leq y \leq 5$$ 4. **Interpretation:** These inequalities mean that any point $(x,y)$ inside or on the boundary of the shaded rectangle satisfies both conditions simultaneously. **Final answer:** $$-2 \leq x \leq 2 \quad \text{and} \quad 2 \leq y \leq 5$$