In the given problem, the number is taken by a variable x.
Let us break the given statement into smaller parts.
First part : " product of a number, x, and five"
Product represents multiplication operation.
Therefore, product of a number, x, and five can be written as an expression
5*x = 5x.
Second part : "half the sum of the number and two".
Half could be represent by fraction 1/2, and sum of a number x and 2 by (x+2).
Therefore, second part of the expression could be written as
1/2 (x+2).
On combining both parts together, we get final expression
5x = 1/2 (x+2)
Therefore, option B is correct, that is 5x = 1/2 (x+2).
