5. For any set $S$, let $|S|$ denote the number of elements in the set, and let $n(S)$ denote the number of subsets of set $S$. If $A, B, C$ are three sets that satisfy the following conditions:
(1) $n(A)+n(B)+n(C)=n(A \cup B \cup C)$;
(2) $|A|=|B|=100$.

Find the minimum value of $|A \cap B \cap C|$.