The equation that represents the relationship between Ben's age and Luciana's age is y = 5 + x. So the correct option is C.
The equation that represents the relationship between Ben's age and Luciana's age is C) y = 5 + x.
Here's why:
* We are given that Ben is five years younger than Luciana. This means that Ben's age can be found by subtracting 5 from Luciana's age.
* In mathematical terms, if Luciana's age is represented by x, then Ben's age can be represented by y = x - 5.
* However, the question asks for the equation that represents the relationship between Ben's age and Luciana's age, not the other way around.
* To reverse the equation, we can simply swap x and y. This gives us the equation y = 5 + x.
Therefore, option C) is the correct answer.