Mathematical notation for "in the domain of"

Question

Is there a mathematical symbol that lets me say something like "5 is in the domain of f" or "5 is NOT in the domain of f"?

Answer 1

$x \in \text{dom} \ f$, $x \notin \text{dom} \ f$

In your case, we'd have $x=5$.

Answer 2

In computability theory the notation $f(x)\downarrow$ is often used for $x \in dom(f)$. The terminology that is used in this context is that the computation of $f(x)$ converges. The corresponding notation for $x \not \in dom(f)$ is $f(x) \uparrow$. I rather like this notation but it is seldom encountered outside of computability theory