To find $f \circ g(5)$, also written as $fog(5)$, follow these steps:

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Step 1: Recall the composition definition

The function $fog(x)$ represents $f(g(x))$.
Here, you have $fog(x) = -5(x^2 - 4) - 1$, which suggests $g(x) = x^2 - 4$ and $f(g(x)) = -5(g(x)) - 1$.

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Step 2: Plug $x = 5$ into $g(x)$

The inner function is $g(x) = x^2 - 4$. Substituting $x = 5$:
$g(5) = 5^2 - 4 = 25 - 4 = 21$

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Step 3: Evaluate $f(g(x))$ using $g(5) = 21$

Since $fog(x) = -5(g(x)) - 1$, substitute $g(5) = 21$:
$fog(5) = -5(21) - 1$

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Step 4: Simplify

$fog(5) = -105 - 1 = -106$

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Final Answer:

$fog(5) = -106$

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Would you like more details on any step? Here are some follow-up questions to consider:

1. Can you explain the concept of function composition in more depth?
2. How can you verify $g(x) = x^2 - 4$ fits within $fog(x)$?
3. What happens if $g(x)$ changes to another function?
4. How can graphing $fog(x)$ help visualize the composition?
5. What if $x$ were a different value, like $x = -5$?

Tip: Always simplify the inner function first before applying the outer function in compositions!