GAIC Math 2024 Problem 30

If the sum of the digits of a natural number $\alpha$ equals 7, then $a$ is called an "auspicious number". Arrange all "auspicious numbers" in ascending order $a_1,a_2,a_3,\cdots$, if $a_n=2005$, then $a_{5n}$=\underline{\hspace{2cm}}.