The function $f(x) = \frac{5}{x}$ is undefined at $x = 0$ because division by zero is not allowed.

Since $f(0)$ does not exist, the graph of $f(x) = \frac{5}{x}$ cannot pass through the point $(0, 0)$.

Therefore, the statement that $f(x)$ has an intercept at $(0, 0)$ is false.