The given function is:

$f(x) = \frac{8}{x + 5}$

To find the inverse function, follow these steps:

Step-by-Step Solution:

1. Write $y = f(x)$: $y = \frac{8}{x + 5}$

2. Swap $x$ and $y$: $x = \frac{8}{y + 5}$

3. Solve for $y$: $x(y + 5) = 8$ $xy + 5x = 8$ $xy = 8 - 5x$ $y = \frac{8 - 5x}{x}$

4. Thus, the inverse function is: $f^{-1}(x) = \frac{8 - 5x}{x}$

Would you like more details or have any questions? Here are five related questions you might find useful:

1. How can you verify that two functions are inverses of each other?
2. What is the domain and range of the inverse function $f^{-1}(x)$?
3. What transformations are involved when finding the inverse of a function like this?
4. How do the vertical asymptotes of $f(x)$ and $f^{-1}(x)$ compare?
5. How would you graph the original function and its inverse on the same coordinate plane?

Tip: Always check the domain restrictions of the original function to ensure the inverse function is correctly defined.