To find $f(-5)$, we need to use the definition of the function $f(x)$ at $x = -5$.

From your piecewise function:

• $f(x) = -(x + 7)^2 - 2$ when $x \neq -5$
• $f(x) = 1$ when $x = -5$

Since you are looking for $f(-5)$, we use the second part of the function definition where $f(x) = 1$ for $x = -5$.

Thus, $f(-5) = 1$.

Would you like further explanation on this?

Here are 5 related questions:

1. What is the value of $f(x)$ when $x = -4$?
2. How does the function behave for values close to $x = -5$?
3. What would $f(x)$ equal for $x = 0$?
4. How would you graph this piecewise function?
5. Can we discuss the significance of piecewise functions?

Tip: When working with piecewise functions, always carefully check the conditions for each segment to avoid confusion.