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Let's break down the given expression:

We are asked to simplify the following polynomial expression:

\[
\frac{x^2 - 1}{x + 1} \cdot \frac{x + 5}{5x - 5}
\]

### Step 1: Factor each part of the expression

- \( x^2 - 1 \) is a difference of squares, so we can factor it as:
  \[
  x^2 - 1 = (x - 1)(x + 1)
  \]

- The denominator \( 5x - 5 \) has a common factor of 5, so we can factor it as:
  \[
  5x - 5 = 5(x - 1)
  \]

Now the expression becomes:
\[
\frac{(x - 1)(x + 1)}{x + 1} \cdot \frac{x + 5}{5(x - 1)}
\]

### Step 2: Simplify the expression

- Cancel the common factor \( x + 1 \) from the numerator and denominator:
  \[
  \frac{(x - 1)}{1} \cdot \frac{x + 5}{5(x - 1)}
  \]

- Cancel the common factor \( x - 1 \) from both fractions:
  \[
  1 \cdot \frac{x + 5}{5}
  \]

This simplifies to:
\[
\frac{x + 5}{5}
\]

### Final Answer:

The simplest form of the given polynomial expression is \( \frac{x + 5}{5} \), which corresponds to **option B**.

Would you like more details or have any questions? 

Here are 5 related questions to explore further:
1. How do you identify common factors in polynomial expressions?
2. What are the steps to simplify fractions involving polynomials?
3. How can the difference of squares help in factoring polynomials?
4. When should you cancel terms in a rational expression?
5. How can factoring help in solving equations involving polynomials?

**Tip:** Always check for common factors before simplifying rational expressions to avoid unnecessary complexity.

Write the polynomial expression in simplest form: (x^2 - 1)/(x + 1) * (x + 5)/(5x - 5).

Learn how to simplify the polynomial expression (x^2 - 1)/(x + 1) * (x + 5)/(5x - 5) by factoring and canceling common terms. This step-by-step solution covers key algebraic concepts and methods for simplifying rational expressions.

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