7.85 Given the following $5 \times 5$ number table
$$
\left(\begin{array}{ccccc}
11 & 17 & 25 & 19 & 16 \\
24 & 10 & 13 & 15 & 3 \\
12 & 5 & 14 & 2 & 18 \\
23 & 4 & 1 & 8 & 22 \\
6 & 20 & 7 & 21 & 9
\end{array}\right)
$$

Try to select 5 elements from this number table such that no two of them are in the same row or column, and make the smallest one as large as possible. Prove the correctness of your selected answer.
[Solution] Since the number table has only 4 edges, according to the problem, at most 4 elements can be selected from the edges. Therefore, after removing the four edges, at least one element should still be selected from the central $3 \times 3$ number table. It is easy to see that the maximum value of this element is 15.
Then, select four numbers greater than 15 from the 4 edges of the number table: $25, 18, 23, 20$.
In fact, after selecting 15, 25 must be selected in the third column, 18 must be selected in the third row, and 23 and 20 must be selected in the fourth and fifth rows, respectively. Thus, the 5 selected elements are the only solution that meets the requirements of the problem.