【Solution】Solution: According to the analysis, there are only three scenarios for these five numbers: (1) three even numbers and two odd numbers, in which case the sum of the five numbers is even; (2) two even numbers and three odd numbers, in which case the sum of the five numbers is odd; (3) one even number and four odd numbers, in which case the sum of the five numbers is even.

The numbers with the same product are: $3 \times 4=2 \times 6, 1 \times 6=2 \times 3$; clearly, the only pair with the same product but different parity is $3 \times 4$ and $2 \times 6$, so the remaining three numbers are: $1, 5, 7$,
$\therefore 1 \times 5 \times 7 \times 3 \times 4=1 \times 5 \times 7 \times 2 \times 6=420$, at this point, the five numbers with a product of 420 could be $1 \times 5 \times 7 \times 3 \times 4, 1+5+7+3+4=20$ which is even; $1 \times 5 \times 7 \times 2 \times 6, 1+5+7+2+6=21$ which is odd, meeting the requirement. Therefore, the product of the five numbers chosen by Bènbèn is 420.
9. (10 points) Congcong performs a math magic trick, writing down $1, 2, 3, 4, 5, 6, 7$ on the blackboard, and asks someone to choose 5 of these numbers. Then, the person calculates the product of these 5 numbers and tells Congcong the result, and Congcong guesses the numbers chosen. When it was Bènbèn's turn to choose, Congcong couldn't even determine whether the sum of these 5 numbers was odd or even. What is the product of the 5 numbers Bènbèn chose? $\qquad$