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?
“One of the ways to look at division is as how many of the smaller number you need to make up the bigger number, right?  So 20/4 means: how many groups of 4 do you need to make 20?  If you want 20 apples, how many bags of 4 apples do you need to buy?

So for dividing by 0, how many bags of 0 apples would make up 20 apples in total?  It’s impossible — however many bags of 0 apples you buy, you’ll never get any apples — you’ll certainly never get to 20 apples!  So there’s no possible answer, when you try to divide 20 by 0.”
Explain him the problems, don't enforce him as an "official view".

Explain him, what are the problems of the division by zero.

Let him to think about a possible solution.

You might also explain, that also the negative numbers don't have a suqare root, but this problem had a solution, the imaginary numbers. Let him try to think about a similar solution for the division by zero.