Tropical Hello Kitty has a quest for you! She is located in Sunshine Shores. Click her, and she will give you a quest.
The 5 bows are located:
In Sunshine Shores Cave on the lifeguard chair
In the Friendship Forest Entrance near the bench on the right
In the Pawsitively Green Center in the top left corner on the bench
In the Pawlette Coufur Boutique in the bottom left side of the screen
In the Bear University Classroom on a desk