The Scales and the Counterfeit Coin

This problem was given to me many years ago by my friends Heather and Ross.

You have a bag of 117 coins of which 1 is a counterfeit. This counterfeit is identical to the other coins except that it is slightly
heaver or lighter than the real coins. You do not know which. You are given a set of precision balance scales, but no standard weights. You may use it 5 times. Can you isolate the counterfeit and how ?

If that is not hard enough, how would you isolate the counterfeit from 118 or even 119 coins?

The solution will arrive in two weeks.

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