5. For $k$ positive real numbers $a_{1}, a_{2}, \cdots, a_{k}$, the quantity $\sqrt{\frac{a_{1}^{2}+a_{2}^{2}+\cdots+a_{k}^{2}}{k}}$ is called the quadratic mean of these $k$ numbers. Let $A_{n}$ denote the quadratic mean of all numbers in $1,2, \cdots, 2009$ that are divisible by $n$. Then the order of $A_{2} 、 A_{3} 、 A_{5} 、 A_{7}$ from largest to smallest is $(\quad$.
(A) $A_{2}>A_{3}>A_{5}>A_{7}$
(B) $A_{2}<A_{3}<A_{5}<A_{7}$
(C) $A_{3}<A_{2}<A_{5}<A_{7}$
(D) $A_{5}<A_{3}<A_{2}<A_{7}$
5.D.
$$
\begin{array}{l}
A_{2}=\sqrt{\frac{2^{2}+4^{2}+\cdots+2008^{2}}{\frac{2008}{2}}} \\
=2 \sqrt{\frac{1^{2}+2^{2}+\cdots+1004^{2}}{1004}} \\
=2 \sqrt{\frac{1005 \times 2009}{6}}=\sqrt{\frac{2010 \times 4018}{6}} \text {, } \\
A_{3}=\sqrt{\frac{3^{2}+6^{2}+\cdots+2007^{2}}{\frac{2007}{3}}} \\
=3 \sqrt{\frac{1^{2}+2^{2}+\cdots+669^{2}}{669}} \\
=3 \sqrt{\frac{670 \times 1339}{6}}=\sqrt{\frac{2010 \times 4017}{6}} \text {, } \\
A_{5}=\sqrt{\frac{5^{2}+10^{2}+\cdots+2005^{2}}{\frac{2005}{5}}} \\
=5 \sqrt{\frac{1^{2}+2^{2}+\cdots+401^{2}}{401}} \\
=5 \sqrt{\frac{402 \times 803}{6}}=\sqrt{\frac{2010 \times 4015}{6}} \text {, } \\
A_{7}=\sqrt{\frac{7^{2}+14^{2}+\cdots+2009^{2}}{\frac{2009}{7}}} \\
=7 \sqrt{\frac{1^{2}+2^{2}+\cdots+287^{2}}{287}} \\
=7 \sqrt{\frac{288 \times 575}{6}}=\sqrt{\frac{2016 \times 4025}{6}} \text {. } \\
\end{array}
$$

Therefore, $A_{5}<A_{3}<A_{2}<A_{7}$.