5. Consider the set $S=\{1,2, \cdots, 10\}$ and all its non-empty subsets. If the number of even numbers in a non-empty subset is no less than the number of odd numbers, then this subset is called a "good subset". Therefore, the number of good subsets is ( ) .
(A) 631
(B) 633
(C) 635
(D) 637
5.D.

Suppose a good subset contains $i(i=1,2,3,4,5)$ even numbers. Then the number of odd numbers can be $j(j=0,1, \cdots, i)$.
Therefore, the number of good subsets is
$$
\begin{array}{l} 
\sum_{i=1}^{5}\left(C_{5}^{i} \sum_{j=0}^{i} C_{5}^{j}\right) \\
= C_{5}^{1}\left(C_{5}^{0}+C_{5}^{1}\right)+C_{5}^{2}\left(C_{5}^{0}+C_{5}^{1}+C_{5}^{2}\right)+ \\
C_{5}^{3}\left(C_{5}^{0}+C_{5}^{1}+C_{5}^{2}+C_{5}^{3}\right)+ \\
C_{5}^{4}\left(C_{5}^{0}+C_{5}^{1}+C_{5}^{2}+C_{5}^{3}+C_{5}^{4}\right)+ \\
C_{5}^{5}\left(C_{5}^{0}+C_{5}^{1}+C_{5}^{2}+C_{5}^{3}+C_{5}^{4}+C_{5}^{5}\right) \\
= 637 .
\end{array}
$$