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The limit you have provided is:

\[
\lim_{x \to \infty} \left( \frac{25}{(x + 5)^2} \right)
\]

### Solution:

1. As \(x \to \infty\), the expression \(x + 5\) grows very large, and specifically, \(x + 5 \to \infty\).
2. The square of a large number \( (x + 5)^2 \) also approaches infinity.
3. Now, observe the fraction: \( \frac{25}{(x + 5)^2} \). As the denominator grows larger and larger, the value of the whole fraction gets smaller and smaller.

Thus:

\[
\lim_{x \to \infty} \frac{25}{(x + 5)^2} = 0
\]

### Final Answer:
\[
\boxed{0}
\]

Would you like further details on the steps involved or have any other questions?

Here are 5 related questions to expand your understanding:
1. How do limits behave when approaching infinity in rational functions?
2. What would happen if the exponent were different in the denominator, e.g., \( (x + 5)^3 \)?
3. How do we handle limits when there is a square root involved?
4. What is the significance of the highest degree term when calculating limits at infinity?
5. How can L'Hopital's rule be applied to limits of rational functions at infinity?

**Tip:** When dealing with limits as \(x \to \infty\), pay close attention to how fast the denominator grows relative to the numerator!

Learn how to calculate the limit of the rational function 25 / (x + 5)^2 as x approaches infinity. The solution explains key concepts in limits, asymptotic behavior, and rational functions, suitable for students in Grades 10-12.

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