So here's what we know:
a = b - 1 (the first integer is 1 less than the middle)
c = b + 1 (the last integer is 1 more than the middle)
a + c = 5b - 57 (the first and last's sum is equal to 57 less than 5 times the middle)
We have values for some of our variables, so plug them in:
b - 1 + b + 1 = 5b - 57
2b = 5b - 57
Are you able to isolate b from here? Subtract 5b from both sides, then divide both sides by the remaining coefficient to get your answer for the middle integer.