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The problem you have provided is asking to evaluate the following limit:

\[
\lim_{x \to 5} \frac{x^2 - 10x + 25}{x^2 - 5}
\]

### Step-by-step solution:

1. **Simplify the numerator:**
   The numerator is a quadratic expression \(x^2 - 10x + 25\), which can be factored as:
   \[
   x^2 - 10x + 25 = (x - 5)^2
   \]

2. **Denominator analysis:**
   The denominator is \(x^2 - 5\), which cannot be factored further directly, but it is already simplified.

Thus, the expression becomes:

\[
\lim_{x \to 5} \frac{(x - 5)^2}{x^2 - 5}
\]

3. **Direct substitution:**
   If we try to directly substitute \(x = 5\) into the expression, the numerator becomes \( (5 - 5)^2 = 0 \) and the denominator becomes \( 5^2 - 5 = 25 - 5 = 20 \).

Hence, we have:

\[
\frac{0}{20} = 0
\]

### Conclusion:
The value of the limit is \( \boxed{0} \).

Would you like further details or clarifications on any step?

Here are five related questions you might find useful:
1. What is the general process for factoring quadratic expressions?
2. How do you handle limits that result in indeterminate forms like \(0/0\)?
3. How can you apply L'Hopital's Rule to limits involving fractions?
4. What are the common techniques to simplify complex limits?
5. Can all limits be evaluated by direct substitution?

**Tip:** Always check if direct substitution is possible before attempting more complex limit-solving techniques like factoring or L'Hopital's Rule.

Evaluate: lim (x → 5) (x^2 - 10x + 25) / (x^2 - 5)

Learn how to evaluate the limit of the expression (x^2 - 10x + 25)/(x^2 - 5) as x approaches 5. This solution involves simplifying quadratic expressions and applying direct substitution techniques. Suitable for high school students in Grades 11-12.

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