The problem you've provided involves the binomial expansion of $(a - b)^5$. Using the binomial theorem, the expansion of $(a - b)^5$ can be written as:

$(a - b)^5 = \sum_{k=0}^{5} \binom{5}{k} a^{5-k}(-b)^k$

This formula expands as:

$a^5 - 5a^4b + 10a^3b^2 - 10a^2b^3 + 5ab^4 - b^5$

Now, let’s identify the specific terms mentioned in your problem:

1. Term with $a^2$: The term containing $a^2b^3$ is the fourth term in the expansion, which is: $-10a^2b^3$ Therefore, the coefficient is $-10$.

2. Term with $b^4$: The term containing $ab^4$ is the fifth term in the expansion, which is: $5ab^4$ Therefore, the coefficient is $5$.

Thus:

• The term in $a^2$ is $-10a^2b^3$,
• The term in $b^4$ is $5ab^4$.

Would you like further clarification or a breakdown of any part of this? Here are some follow-up questions you might find useful:

1. How does the binomial theorem work for different powers?
2. What is the general formula for a binomial expansion?
3. How do you determine the coefficients in a binomial expansion?
4. Can you explain the meaning of the binomial coefficient $\binom{n}{k}$?
5. How does the sign change affect the terms in the expansion?

Tip: Always remember that in binomial expansions, the signs alternate depending on whether the binomial has a negative or positive term inside!