5. For any subsets $A, B$ of $X_{n}$ ( $A, B$ can be the same), find $\sum_{A, B \subseteq X}|A \cap B|$, where $|A|$ denotes the number of elements in $A$.


(The number of set pairs $(A, B)$ such that $|A \cap B|=k$ is $\mathrm{C}_{n}^{k} 3^{n-k}$, from which we get $\left.\sum_{A, B \subseteq X_{n}}|A \cap B|=n \times 4^{n-1}.\right)$