How to delete songs from iPhone 5s?

I just got the new iPhone and bought some individual songs that I don't want anymore. I've tried swiping to delete them and deleting them from the playlist section. I got them off once but they came back after like a week.

They're probably sync'd with either your iTunes account/program or iCloud if you're configured to back up your items to that. If you're sync'ing your phone with iTunes, you'll need to remove them from there and sync your phone again to remove them from the device.