The equation given is:

$|x + 5| = -3$

Let's analyze this step by step:

1. Absolute Value Properties: The absolute value of any real number is always non-negative. This means that $|x + 5| \geq 0$ for all values of $x$. Therefore, it is impossible for $|x + 5|$ to equal a negative number like $-3$.

2. No Solution: Since the absolute value of a number can never be negative, the equation has no solution. In other words, there is no value of $x$ that satisfies $|x + 5| = -3$.

Thus, the correct answer is A) $\emptyset$ (no solution).

Would you like more details, or do you have any further questions?

Here are 5 follow-up questions for further learning:

1. What would be the solution if the equation was $|x + 5| = 3$?
2. Can absolute value equations ever have negative solutions?
3. How can we graphically represent an absolute value function?
4. What happens if the absolute value function is less than a positive number, for example, $|x + 5| < 4$?
5. How do you solve absolute value inequalities?

Tip: Always remember that absolute values are non-negative, so they can never equal a negative number.