Answer:
For the product of those five integers to be less than zero, at least one of them has to be a negative number, but since they are consecutive, it follows that all of them are negative, since including 0 would result in a non-negative product (that is, 0). These negative numbers have to add up to -25, and the following values correspond to that target value:
[−7,−6,−5,−4,−3][−7,−6,−5,−4,−3]
To get there - if the smallest of those integers is xx, then the following is true:
x+x+1+x+2+x+3+x+4=−25=>5x=−35=>x=−7
