Five. (12 points) Try to find the largest and smallest seven-digit numbers that can be divided by 165, formed by the 7 digits $0,1,2,3,4,5,6$ without repetition (require the reasoning process to be written out).

Find the largest and smallest seven-digit numbers that can be formed using the digits $0,1,2,3,4,5,6$ without repetition, which are divisible by 165 (the reasoning process must be included).
Five, since $165=3 \times 5 \times 11$, the number we are looking for must be a multiple of 3, 5, or 11. Also, $0+1+2+3+4+5+6=21$. Therefore, the sum of these seven digits is always a multiple of 3.

Let the sum of the four digits in the odd positions be $A$, and the sum of the three digits in the even positions be $B$. Then $|A-B|=11k$ (where $k$ is an integer greater than or equal to 0).
Also, $A+B=21$ and $A, B$ are both positive.
Thus, $|A-B|<21$.
Since $A+B$ is odd, $A-B \neq 0$.

Therefore, $k \neq 0$, so $k=1$.
Thus, one of $A$ and $B$ is 16, and the other is 5.
Since $0+1+2+3=6$, $A$ cannot be 5, so $A$ is 16, and $B$ is 5.

Among these seven numbers, the only pairs that sum to 5 are $0,1,4$ or $0,2,3$.
(1) $B=0+1+4, A=2+3+5+6$,
(2) $B=0+2+3, A=1+4+5+6$.
Since 0 is always in one of the three groups (i.e., even positions), 0 cannot be the leading digit. Also, since the number we are looking for is a multiple of 5, the last digit must be 5. Therefore, the smallest number is 1042635, and the largest number is 6431205.
(Provided by Liu Hanwen, Hubei)