*5. Let $I=\{1,2, \cdots, 100\} . M$ represents the number of subsets of $I$ where the maximum element is 66, $N$ represents the number of subsets of $I$ where the minimum element is 33, and $P$ represents the number of subsets of $I$ where the maximum element is three times the minimum element. Then ( ).
(A) $M<N<P$
(B) $M<P<N$
(C) $N<P<M$
(D) $P<M<N$
5. B.
$M=2^{65}$. Since the set $\{1,2, \cdots, 65\}$ has $2^{65}$ subsets. Each subset, when 66 is added, results in all subsets with the maximum element being 66. Similarly, all subsets of $\{34, 35, \cdots, 100\}$, when 33 is added, result in all subsets with the minimum element being 33. Therefore, $N=2^{67}$. $P$ is the number of subsets of the form: $\{1, \cdots, 3\},\{2, \cdots, 6\},\{3, \cdots, 9\}, \cdots,\{33, \cdots, 99\}$. $P=2^{1}+2^{3}+2^{5}+\cdots+2^{65}=\frac{2\left(4^{33}-1\right)}{4-1}=\frac{2^{67}-1}{3}$, thus $2^{65}<P<2^{67}$.