It will take 72 days to be the correct time again.
We will set up a proportion for this. The first ratio will be 5/6 (5 minutes off every 6 hours). In order to be correct again, the clock must be off by a full 24 hours. 24 hours *60 minutes = 1440 minutes; the second ratio of the proportion is 1440/x:
5/6 = 1440/x
5*x = 6*1440
5x=8640
Divide both sides by 5:
5x/5 = 8640/5
x=1728
It will take 1728 hours. This is 1728/24 = 72 days.
