1. **Identify the domain and range of** $y=\sqrt{x-2}+5$. 2. **Domain**: The expression inside the square root must be non-negative. $$x-2 \geq 0$$ $$x \geq 2$$ So, the domain is $[2, \infty)$. 3. **Range**: Since $\sqrt{x-2} \geq 0$, the smallest value of $y$ is when $\sqrt{x-2}=0$. $$y_{min} = 0 + 5 = 5$$ As $x$ increases, $\sqrt{x-2}$ increases without bound, so the range is $[5, \infty)$. **Final answer:** - Domain: $[2, \infty)$ - Range: $[5, \infty)$