The keys are:

1.

How do you spell "mousetrap" with only three letters? "Cat"
2. What kind of dog has no tail? Hotdog
3. What kind of bushes do rabbits hide when it is a rainy day? Wet ones
4. How do you keep a Rhino from charging? Take away his/her credit cards
5. What looks like a cat, sounds like a cat, moves like a cat, but it isn't a cat? A kitten