The given problem states:

• $a + b = ab = 5$.
• We are asked to find the value of $a^2b + ab^2$.

Solution:

First, observe the following:

The expression $a^2b + ab^2$ can be rewritten as:

$a^2b + ab^2 = ab(a + b)$

Now, using the information given in the problem:

• $a + b = 5$,
• $ab = 5$,

Substituting these values into the expression:

$ab(a + b) = 5 \times 5 = 25$

Thus, the value of $a^2b + ab^2$ is 25.

Final Answer:

The correct answer is $\boxed{25}$.

Would you like further explanation or have any questions? Here are 5 related questions to deepen your understanding:

1. How do you expand the expression $a^2b + ab^2$ using factoring techniques?
2. What other forms can we express the equation $a + b = ab = 5$ in?
3. How does the solution change if $a + b$ and $ab$ have different values?
4. What techniques can you use to solve equations involving multiple variables like this one?
5. Can you generalize this problem for any arbitrary value of $a + b$ and $ab$?

Tip: Always look for ways to factor common terms in expressions to simplify calculations.