5. For the set $S=\{1,2, \cdots, 18\}$, a five-element subset $S_{1}$ $=\left\{a_{1}, a_{2}, a_{3}, a_{4}, a_{5}\right\}$ is such that the difference between any two elements is not 1. The number of such subsets $S_{1}$ is ().
(A) $C_{17}^{4}$
(B) $C_{15}^{4}$
(C) $C_{13}^{5} \quad-\quad+\quad \begin{array}{l}5\end{array}$
(D) $C_{14}^{5}$
5. (D).

Let the subset $S^{\prime}=\left\{a_{1}, a_{2}-1, a_{3}-2, a_{4}-3, a_{5}-4\right\}$. Then $S^{\prime}$ corresponds one-to-one with $S_{1}$, and $S^{\prime}$ is a five-element subset of $\{1,2, \cdots, 14\}$.