First of all, I have to state this: Unless your child is going for Math Olympiad or something, he or she is doing the wrong book. This is A-Level standard, minimum.

Secondly, I assumed that 5 appears twice in the number 55. If this question were to ask "How many numbers from 40000 to 43000 contain the digit 5?" the working would be more complicated than it is right now, because I would need to eliminate all the double/triple counts.