Problem 6 (2021 AIME II)

For any finite set $S$, let $|S|$ denote the number of elements in $S$. Find the number of ordered pairs $(A, B)$ such that $A$ and $B$ are (not necessarily distinct) subsets of $\{1, 2, 3, 4, 5\}$ that satisfy $|A| \cdot |B| = |A \cap B| \cdot |A \cup B|$