### Instruction: Find the domain of the function
\[h(x) = \frac{3x - 1}{\sqrt{x - 5}}.\].### Response: The domain of a function is the set of all possible inputs (x-values) that make the function defined and real.
To find the domain of h(x), I need to avoid any x-values that would make the denominator zero or negative, since that would result in an undefined or imaginary expression under the square root.
Therefore, I need to solve the inequality
\[x - 5 > 0\]
To do that, I can simply add 5 to both sides, and get
\[x > 5\]
This means that any x-value greater than 5 is a valid input for h(x), and any x-value less than or equal to 5 is not.
So, the domain of h(x) is the interval (5, infinity), using parentheses to indicate that 5 is not included.