1. **State the problem:** We have a function $f(x) = \sqrt{x - 5}$ and we want to find the equation of its reflection $g(x)$ about the line $y = x$. 2. **Recall the reflection rule:** Reflecting a function about the line $y = x$ swaps the roles of $x$ and $y$. So if $y = f(x)$, then the reflection satisfies $x = f(y)$. 3. **Apply the reflection:** Given $y = \sqrt{x - 5}$, swap $x$ and $y$ to get: $$x = \sqrt{y - 5}$$ 4. **Solve for $y$:** Square both sides to remove the square root: $$x^2 = y - 5$$ Add 5 to both sides: $$y = x^2 + 5$$ 5. **Interpretation:** The reflected function is: $$g(x) = x^2 + 5$$ where $g(x)$ is the reflection of $f(x)$ about the line $y = x$. 6. **Domain and range:** The original function $f(x)$ has domain $x \geq 5$ and range $y \geq 0$. After reflection, $g(x)$ has domain $x \geq 0$ and range $y \geq 5$. **Final answer:** $$g(x) = x^2 + 5$$ where $g(x)$ is the reflection of $f(x) = \sqrt{x - 5}$ about the line $y = x$.