How to delete songs completely off an iphone 5s?

I downloaded a song from the itunes store on my phone and whenever I try and delete it it's still there but faded and won't let me play it except if I download it again. Is there a way to erase the songs completely from my list b/c it's getting annoying.

You can use your laptop and manage your library in iTunes OR you can go on your phone, go to settings, go to Music, and then unclick where it says "Show all music". Hope this helps!