How do you define discrete math to a 5 years old kid in a nontechnical way?
It seems to me even the formal definition of discrete math is vague for me.
Preliminary question: Do you have a 5 years old child who has asked you: "Dad, what do you do at work ?" You have answered automaticaly "I do discrete maths", and now you have to explain him/her ?
At 5, a child is able to master the sequence of numbers, have a certain consciousness of them being an infinite number, and that's all. He/she doesn't master their writing (or he/she knows how to write figures/digits from 1 to 9, but not give a meaning to "12" for example as being "twelve"). This is mastered 2 or 3 years later.
This what is discrete maths for a child IMHO. Of course, doing graphs (there are games that more or less are based on graphs) is doing discrete maths...
For explaining the difference with "continuous maths", I see the use of a sliders like you find more and more everywhere (in Geogebra for example)...
It's all the ideas that come to my mind this evening...
In a subtle way you can introduce discrete math concepts by telling your 5 years old kid, "learn to count and draw a square house like this":
Demonstration of the cottage (Farm Show is valid too :).
Later you can replace the cottage by a pyramid:
Pyramid's proof of Pythagoras (Egyptian or Aztec one..)
And meanwhile with the help of cartoons like Smecytes, you can invite your kid to take a cup of TEA in one of those buildings waiting for an imaginary alien who would come from the outer space to teach more advanced concepts related to Diophantine equations like the ABC conjecture (ÑAN in spanish), FLT & more:
Equivalence Theory (ET for friends, proofs %&8 but still editing the style of the document located at Wolfram Cloud, check my twitter timeline for the link.).