1. **State the problem:** We are given the function $y=\log_5(x-10)$ with the domain $3 \leq x \leq 5$. We need to find the minimum and maximum values of $y$ on this domain. 2. **Check the domain:** The function $\log_5(x-10)$ is defined only when the argument $x-10 > 0$, i.e., $x > 10$. However, the given domain is $3 \leq x \leq 5$, which does not satisfy $x > 10$. 3. **Conclusion:** Since the domain $3 \leq x \leq 5$ does not satisfy the condition for the logarithm to be defined, the function $y=\log_5(x-10)$ is not defined on this interval. Therefore, there is no minimum or maximum value of $y$ for $3 \leq x \leq 5$ because the function is not defined there.