As the required sum is 5, keep 5 as one of the integers and write two pairs of integers which are additive inverses of each other.

For example, 5 + [2+(–2)]+[3+(–3)]= 5.

Thus, the required five integers are 5, 2, –2, 3, –3

There can be many combinations of five integers, such as 5, 3, –3, 6, –6 or 4, 2, 3, –3, –1 etc., whose sum is 5.