AIME 2021b Problem 6

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 $$|A| \cdot |B| = |A \cap B| \cdot |A \cup B|$$