You start with 3 songs in your Katamari Collection. Once you play through a few levels you'll unlock more. When you start the level, it will tell you if the song is new in the bottom left hand corner of the screen. Go to your Katamari Collection and listen to 5 songs. You don't have to listen to them all the way through. Let them play for a few seconds then go back. Once you listened to 5 songs, exit and you'll unlock the trophy.