AMC 10 2022b Problem 16

The diagram below shows a rectangle with side lengths $4$ and $8$ and a square with side length $5$. Three vertices of the square lie on three different sides of the rectangle, as shown. What is the area of the region inside both the square and the rectangle?

$\textbf{(A) }15\dfrac{1}{8} \textbf{(B) }15\dfrac{3}{8} \textbf{(C) }15\dfrac{1}{2} \textbf{(D) }15\dfrac{5}{8} \textbf{(E) }15\dfrac{7}{8}$