Have I got the right understanding of the mu operator? I have a homework problem that says:

For $g(x,y)=xy-5$ compute $h(x) = \mu y(g(x,y))$ and determine its domain.

I was under the impression that this means the least y such that $g(x,y)=0$, so then $y = \frac{5}{x}, D=\{x \in \mathbb{N}, x \neq 0\}$

So $h(x)=\frac{5}{x}$?
Hint: $h(x)$ is always a non-negative integer (whenever it's defined).

As a side note, usually primitive recursive functions are assumed to be non-negative, and so $\max(xy-5,0)$ is more usual than what you wrote.