we assume that the problem is asking to solve for all five integers

let 'n' represent the first integer, then 'n+1', 'n+2', 'n+3' and 'n+4' represents the next four consecutive integers

sum of first and fifth integer is one less than three times the fourth:

(n + n+4) = 3(n+3) - 1

2n + 4 = 3n + 9-1

n = -4

the integers are -4, -3, -2, -1 and 0