How do you explain to a 5th grader why division by zero is meaningless? I wish to explain my younger brother: he is interested and curious, but he cannot grasp the concepts of limits and integration just yet. What is the best mathematical way to justify not allowing division by zero?

You shouldn't try to do that. Instead make counter question. 
"What should it be, then?" and let them think about it.

(Lengthy) justification: There are many important concepts in math you can come up with if you start experimenting with multiplication. Take for example area of a rectangle. You multiply the sides. Area of a curve? You take the integral. What is an integral? Well Riemann imagined thin thin slices, almost infinitely thin, actually. The idea that we can calculate area of these slices where one side is so tiny it almost is 0. If we disqualify limits, or the idea of multiplying something "almost 0" to be 0 then we would have a tougher time coming up with an excuse to investigate integrals, which have been veeery important to the development of modern technology.
Any kid who could come up with some new interpretation of this could be very valuable.
