7. (10 points) Fill the numbers $1 \sim 25$ into the $5 \times 5$ table shown below. In each row, select the largest number, and in each column, select the smallest number. This way, we have made 10 selections in total. Among these 10 selected numbers, there are at least $\qquad$ distinct numbers.
【Analysis】First, according to the problem, determine that there must be a number which is the largest number in its row and the smallest number in its column; then apply the method of assumption, to conclude that: there do not exist two numbers which are both the largest in their row and the smallest in their column, leading to the conclusion that among the 10 selected numbers, at least 9 are different.

【Solution】Solution: (1) There must be a number which is the largest in its row and the smallest in its column, for example: the number 10 in Figure 1 is the largest number in the 5th row and the smallest number in the 1st column,
(2) If there are two such numbers,

then these two numbers must not be in the same row or the same column,
as the $A$ and $B$ in Figure 2,
by the problem, we can get: $B>C>A>D>B$, which is impossible,
so there do not exist two numbers which are both the largest in their row and the smallest in their column,
so among the 10 selected numbers, there are at least: $10-1=9$ different numbers, hence the answer is: 9.