5. Express 2009 as the difference of squares of two integers. Then the number of different ways to do this is ( ).
(A) 16
(B) 14
(C) 12
(D) 10
5. C.

Let $x^{2}-y^{2}=2009$, that is,
$$
(x+y)(x-y)=2009=7^{2} \times 41 \text {. }
$$

Then 2009 has 6 positive divisors, which are $1$, $7$, $41$,
$49$, $287$, and 2009.
Therefore, the corresponding system of equations is
$$
\left\{\begin{aligned}
x+y= & -1,-7,-41,-49,-287, \\
& -2009,1,7,41,49,287,2009 ; \\
x-y= & -2009,-287,-49,-41,-7, \\
& -1,2009,287,49,41,7,1 .
\end{aligned}\right.
$$

Thus, $(x, y)$ has 12 different representations.