One integer is m.
The other integer is n.
n = 23m + 5
mn = 6732
m = 6732/n
n = 23 * 6732/n + 5
n = 154,836/n + 5
n^2 = 154,836 + 5n
n^2 - 5n - 154,836 = 0
n = [5 +- sqrt(25 + 4 * 154,836)]/2
n = (5 +- 787)/2
n = 396 or n = -391
We discard -391 because the problem is looking for positive integers.
mn = 6732
m = 6732/n = 6732/396
m = 17
Answer: The integers are 17 and 396.
