To evaluate the function $f(x) = -9e^x - 1$ at $x = -5$, substitute $x = -5$ into the function:

$f(-5) = -9e^{-5} - 1$

Now, calculate $e^{-5}$:

$e^{-5} \approx 0.006737947$

So, substitute this into the equation:

$f(-5) = -9 \times 0.006737947 - 1$

$f(-5) \approx -0.060641523 - 1$

$f(-5) \approx -1.0606$

So, $f(-5) \approx -1.0606$ when rounded to four decimal places.

Would you like more details or have any questions?

Here are some related questions you might consider:

1. How does the base of the natural logarithm $e$ affect the function?
2. What happens to $f(x)$ as $x$ becomes very large?
3. How would you differentiate $f(x) = -9e^x - 1$?
4. What is the inverse function of $f(x) = -9e^x - 1$?
5. How would the function change if the coefficient of $e^x$ was different?
6. How does the constant term $-1$ influence the graph of the function?
7. How would you solve for $x$ if $f(x) = 0$?
8. What is the y-intercept of the function $f(x) = -9e^x - 1$?

Tip: When dealing with exponential functions, remember that small changes in the exponent can result in large changes in the value of the function.