Let's solve the problem step by step.

We are asked to evaluate $g(f(-1))$, where the function $f(x) = 5x + 2$ is given.

1. First, compute $f(-1)$: $f(-1) = 5(-1) + 2 = -5 + 2 = -3$ So, $f(-1) = -3$.

2. Next, evaluate $g(f(-1)) = g(-3)$. Unfortunately, the function $g(x)$ is not provided in the image. To find the final result, we would need the definition of $g(x)$.

If you know the function $g(x)$, we can substitute $g(-3)$ and solve the problem completely. Could you provide that information?

Feel free to ask for further details or clarifications. Here are five related questions to consider:

1. How do composite functions like $g(f(x))$ work in general?
2. How would you solve if a different function $f(x)$ were given?
3. What are some common forms of the function $g(x)$?
4. How does the order of function composition affect the result?
5. Can composite functions have practical applications?

Tip: Always evaluate functions from the innermost part outward in compositions, starting with the most nested function.