Oh my gosh. This might have to replace The Monster at the End of This Book as the Best Children's Higher Math Book EVAR! (Although that does have some amazing points to make about self-reference and it's interactive fiction to boot.)

And, mercy, if Alex is five and starting to absorb this, holy cow. You can probably get her started on Flatland next and she's only a year or two away from grasping Knuth's Surreal Numbers.