We are asked to find the value of $(g \circ f)(-2)$, which means we need to compute $g(f(-2))$.

Here are the steps to solve this problem:

1. Find $f(-2)$: The function $f(x)$ is given as: $f(x) = -2x + 7$ Substituting $-2$ into $f(x)$: $f(-2) = -2(-2) + 7 = 4 + 7 = 11$

2. Find $g(f(-2)) = g(11)$: The function $g(x)$ is given as: $g(x) = x^2 - 6x + 5$ Now substitute $11$ into $g(x)$: $g(11) = 11^2 - 6(11) + 5 = 121 - 66 + 5 = 60$

Thus, $(g \circ f)(-2) = 60$.

Would you like further details on any of these steps?

Here are 5 related questions to expand on this:

1. What is the general process for finding the composition of two functions?
2. How can you verify the result of a function composition algebraically?
3. What is the domain of the composed function $(g \circ f)(x)$?
4. How would the result change if we composed $f(g(x))$ instead of $g(f(x))$?
5. Can the order of composition of functions affect the outcome?

Tip: When composing functions, always compute the inner function first and then apply the outer function.