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12 and 7

let x-5 be the first integer
and x be the second integer

(x)(x-5) = 84
x^2 - 5x = 84
subtracting 84 from both sides..
x^2 - 5x - 84 = 0

using the quadratic formula to get the roots of x..
we get x = 12 and x = -7

since the problem asked for Positive integers

x = 12
and x-5 = 7