12. If the sum of the digits of a natural number $a$ equals 7, then $a$ is called a "lucky number". Arrange all lucky numbers in ascending order as $a_{1}, a_{2}, a_{3}, \cdots$, if $a_{n}=2005$, then $a_{5 n}=$ $\qquad$.
The number of $n$-digit lucky numbers corresponds to the number of non-negative integer solutions of $x_{1}+x_{2}+\cdots+x_{n}=7\left(x_{1} \geqslant 1\right)$. Let $x_{1}^{\prime}=x_{1}, x_{2}^{\prime}=x_{2}+1, \cdots, x_{n}^{\prime}=x_{n}+1$, then it corresponds to the number of positive integer solutions of $x_{1}^{\prime}+x_{2}^{\prime}+\cdots+x_{n}^{\prime}=n+6$, which is $C_{n+5}^{n-1}$.
1-digit lucky numbers have only 1; 2-digit lucky numbers have 7; 3-digit lucky numbers have $C_{8}^{2}=28$; 4-digit lucky numbers, where the thousand's place is 1, correspond to the non-negative integer solutions of $x_{2}+x_{3}+x_{4}=6$, which have $C_{8}^{2}=28$ solutions. Thus, 2005 is the 65th lucky number, hence $n=65 \Rightarrow 5 n=325$.
4-digit lucky numbers have $C_{9}^{3}=84$; 5-digit lucky numbers have $C_{10}^{4}=210$. Since $210+84+28+7+1=330$, the 5-digit lucky numbers from largest to smallest are $70000,61000,60100,60010,60001,52000$. Therefore, $a_{5 n}=52000$.