My command of statistics is sadly less than it ought to be, but I think the answer is no. For instance, if the result is binary, i.e. 1 or 0, yes or no, the result cannot be 5% off.
John has covered it in "Sorry, wrong number", but I don't have my copy to hand.

You should be careful to distinguish between P and relative risk. The nearest statistical measure to Margin of Error would be Confidence Interval. See our FAQs.