We need to figure out the value for x-y. Couldn't x-y= 1 or 5? So we are not sure about the (x-y) value?
Also if x is smaller than y and y is smaller than 0 then it means that
x must be -4 and y must be -1 to make (x-y)=-5. The question says "x < y < 0".
Then (x+y) will not equal -1 to make a positive 5. This will not happen because one -4 and other is -1. no way, it will equal -1.
You're correct that x - y doesn't equal -5. Both numbers are negative, so x + y will be more negative (= farther to the left on the number line) than x - y.
Since everything is in terms of integers, that leaves only one possibility: x - y = -1 and x + y = -5. So, sufficient.
(You'll get x = -3 and y = -2, although, as long as you know it guarantees a unique answer, it's unnecessary to solve the system once you've found it).