1. **Stating the problem:** Find the image of point $A(-5,3)$ reflected about the line $x=-2$. 2. **Reflection rule about vertical line $x = a$:** The $x$-coordinate of the image is $x' = 2a - x$, and the $y$-coordinate remains the same $y' = y$. 3. **Apply the formula:** Here, $a = -2$, $x = -5$, $y = 3$. $$x' = 2(-2) - (-5) = -4 + 5 = 1$$ $$y' = 3$$ 4. **Result:** The image point is $A'(1,3)$. 5. **Match with given options:** Option D is $(1,3)$. Final answer: $(1,3)$