AMC 10 2020b Problem 11

Ms. Carr asks her students to read any $5$ of the $10$ books on a reading list. Harold randomly selects $5$ books from this list, and Betty does the same. What is the probability that there are exactly $2$ books that they both select? $\textbf{(A)}\ \frac{1}{8} \textbf{(B)}\ \frac{5}{36} \textbf{(C)}\ \frac{14}{45} \textbf{(D)}\ \frac{25}{63} \textbf{(E)}\ \frac{1}{2}$