To find the inverse of $f(x)$, we switch the roles of $x$ and $y$ and solve for $y$.
So, we have $x = \frac{2y - 1}{y + 5}$.
Cross-multiplying, we get $x(y + 5) = 2y - 1$.
Expanding, we have $xy + 5x = 2y - 1$.
Bringing all the terms with $y$ on one side, we get $xy - 2y = -5x - 1$.
Factoring out $y$, we have $y(x - 2) = -5x - 1$.
Dividing both sides by $(x - 2)$, we get $y = \frac{-5x - 1}{x - 2}$.
Thus, the inverse of $f(x)$ is $f^{-1}(x) = \frac{-5x - 1}{x - 2}$.
Comparing this with the given form of $f^{-1}(x) = \frac{ax + b}{cx + d}$, we have $a = -5$, $b = -1$, $c = 1$, and $d = -2$.
Therefore, $a/c = \frac{-5}{1} = \boxed{-5}$.The answer is: -5
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
The inverse of $f(x) = \frac{2x-1}{x+5}$ may be written in the form $f^{-1}(x)=\frac{ax+b}{cx+d}$, where $a$, $b$, $c$, and $d$ are real numbers.  Find $a/c$.

### Answer:
