1. The problem is to find the set $A = [2, \infty) \cap (-2, 5]$. 2. This means we want the intersection of the two intervals: $[2, \infty)$ and $(-2, 5]$. 3. The interval $[2, \infty)$ includes all numbers $x$ such that $x \geq 2$. 4. The interval $(-2, 5]$ includes all numbers $x$ such that $-2 < x \leq 5$. 5. The intersection $A$ consists of all numbers that satisfy both conditions simultaneously. 6. Since $x$ must be at least 2 and also less than or equal to 5, the intersection is $[2, 5]$. 7. Therefore, the set $A = [2, 5]$. This means $A$ contains all real numbers from 2 to 5, including both endpoints.