She will always need to give you 5 apples. You both need at least 5 apples to begin with, but apart from that it doesn’t matter exactly how many you each have. When she gives you 5 you will have 10 more than her because she will lose 5 and you will gain 5, resulting in a net difference of 10.
For example, if you each have 25 apples and she gives you 5 of hers, she will be left with 20 and you will now have 30, precisely 10 more than she has.
Perform this calculation in your head, mentally adding the numbers as quickly as you can. Start with 1000 and add 40. Now add 1000. Add 30 to that, then add another 1000. Now add 20 to that result. Add another 1000 and finally, add 10 to that. What is the total?
The riddle refers to a variety of meanings of the word fine.
Feeling normal refers to when you feel fine. Extremely thin refers to a fine thread. A punishment refers to being charged a fee. The one who wins refers to an athlete who is physically trained and hardened close to the limit of efficiency. Free from impurity refers to measuring the fineness of precious metals. A keen edge refers to a knife with a fine edge. Refined refers to fine manners or elegance.
Your teeth. You get baby teeth and adult teeth as part of the life package, but once you lose those you get to pay for dentures (or scare small children with your sunken face).