5. If a positive integer can be expressed as the difference of squares of two positive integers, it is called a "wise number" (for example, $3=$ $2^{2}-1^{2}, 16=5^{2}-3^{2}$). It is known that wise numbers, arranged in ascending order, form the following sequence:
$$
\begin{array}{l}
3,5,7,8,9,11,12,13,15,16,17,19,20, \\
21,23,24,25, \cdots .
\end{array}
$$

Then the 2006th wise number is ( ).
(A) 2672
(B) 2675
(C) 2677
(D) 2680
5.C.

Observing and exploring the pattern, we know that all wise numbers, from smallest to largest, can be grouped in sets of three, and starting from the 2nd group, the first number of each group is a multiple of 4. By induction, the first number of the $n$-th group is $4n$ ($n \geqslant 2$).

Since $2006=3 \times 668+2$, the 2006th wise number is the 2nd number in the 669th group, which is $4 \times 669+1=2677$.