The limit problem you've provided involves evaluating the following:

$\lim_{{x \to 5^+}} \frac{-3}{{x - 5}}$

To solve this, let's analyze the behavior as $x$ approaches 5 from the right (i.e., $x \to 5^+$).

1. As $x$ approaches 5 from the right, the denominator $x - 5$ becomes a small positive number (since $x > 5$).
2. The numerator is constantly $-3$, so we have a negative number divided by a small positive number.
3. This results in a very large negative value, heading towards $-\infty$.

Thus, the limit is:

$\lim_{{x \to 5^+}} \frac{-3}{{x - 5}} = -\infty$

The correct answer is A: $-\infty$.

Would you like a more detailed explanation of this type of limit, or do you have any questions?

Here are 5 related questions that could expand on this concept:

1. What happens if we approach the limit from the left ($x \to 5^-$) instead?
2. How does the behavior of limits change with different types of functions, such as polynomials or rational functions?
3. How do you handle limits involving division by zero?
4. What is the significance of the plus or minus sign in a one-sided limit?
5. Can you apply this type of analysis to limits at infinity?

Tip: When evaluating limits of rational functions, always look at the behavior of the numerator and denominator as $x$ approaches the value from different directions.