Prove that if a positive integer $n$ divides the five-digit numbers $\overline{a_1a_2a_3a_4a_5}$, $\overline{b_1b_2b_3b_4b_5}$, $\overline{c_1c_2c_3c_4c_5}$, $\overline{d_1d_2d_3d_4d_5}$, $\overline{e_1e_2e_3e_4e_5}$, then it also divides the determinant $$D=\begin{vmatrix}a_1&a_2&a_3&a_4&a_5\\b_1&b_2&b_3&b_4&b_5\\c_1&c_2&c_3&c_4&c_5\\d_1&d_2&d_3&d_4&d_5\\e_1&e_2&e_3&e_4&e_5\end{vmatrix}.$$