13. (12 points) Fill in all the given number strings into the grid, each number string must be used exactly once, and each cell must contain exactly one digit. The digits of the same number string cannot be separated by shaded cells, and the direction of the number strings is either from top to bottom or from left to right. The figure provides an example, where Figure 2 is the only way to fill Figure 1. Please fill in Figure 3 according to the above rules, then $\overline{\mathrm{ABCDE}}$ is $\qquad$
【Solution】Solution: Since the two five-digit numbers only differ in the middle digit, we can determine 4 digits;
Each three-digit number ends with 0, so they can all be determined;
The only two-digit number ending with 0 is 40, so $E$ can only be 4, and the only number starting with 4 is 40 and 42, with 40 already used, so the left side of $C$ can only be 2, as shown in Figure 1:
There are only two four-digit numbers starting with 1, and the first three digits are all 102, so the first column can be determined as 102;
There is only one four-digit number starting with 2, so 2224 can be determined;
The only three-digit number starting with 4 is 410, so 1 can be determined;
The only three-digit number ending with 10 left is 210, so 2 can be determined;
The only three-digit number starting with 2 and ending with 0 is 220, so $C$ can be determined as 2;
The only two-digit number starting with 2 is 21, so the number below $C$ can only be 1, as shown in Figure 2:
In the third column, the only four-digit number ending with 22 is 1022 and 0022, so the third digit of the two five-digit numbers can only be 0 or 2, so the middle digit of the five-digit number in the first row can only be 0, and the four-digit number in the third column is 0022, so $B$ is 2;

The only four-digit number starting with 0 and ending with 2 left is 0102, so the four-digit number at the bottom of the fifth column can be determined, and the only four-digit number starting with 01 left is 0110, so $D$ can only be 0, as shown in Figure 3:
The three-digit numbers 220, 410, and 210 have all appeared, so the three-digit number in the second-to-last row can only be 120, and the remaining two two-digit numbers are 12 and 11, with 12 only able to be in the second column at the bottom, so $A$ is 1,
as shown in Figure 4:
Thus, the five-digit number can be determined to be 12204,
The answer is: 12204.