Here is a problem I do with my classes when we talk about exponents-- the fifth graders may find it accessible, especially if they have calculators.
Suppose you have a sheet of very thin paper--so thin that 1024 pieces make one inch. Rip the paper in half. Now there are two sheets.Rip the paper again--now there are four sheets, etc. Do this 50 times. How high will the pile of paper be?...a few inches?...a few feet?...a few miles?..as high as the moon? 2^50 is quite large! Maxine