The problem asks which algebraic expressions match the verbal expression "the product of five and a number." Let's break it down:

• "The product" means multiplication.
• "Five" is the number 5.
• "A number" is represented by a variable, such as $b$.

The algebraic expression representing "the product of five and a number" would be $5b$ or $b \cdot 5$.

Now, let's evaluate the options:

• $\frac{5}{b}$: This represents a fraction, not a product. Not correct.
• $5 + b$: This represents a sum, not a product. Not correct.
• $b - 5$: This represents a difference, not a product. Not correct.
• $\frac{b}{5}$: This is a division, not a product. Not correct.
• $b \cdot 5$: This is a product of five and a number. Correct.
• $5b$: This is also a product of five and a number. Correct.

The correct answers are:

• $b \cdot 5$
• $5b$

Would you like a more detailed explanation of any part of this problem?

Here are 5 related questions for further practice:

1. What would be the algebraic expression for "the sum of five and a number"?
2. How do you write the quotient of a number and five algebraically?
3. What is the difference between an algebraic product and a quotient?
4. How do you express "the difference between five and a number" algebraically?
5. How do you represent the product of two different numbers in algebra?

Tip: When translating verbal expressions into algebraic ones, always pay attention to key terms like "sum," "product," "difference," and "quotient," as they define the operations needed.