How to delete songs from my IPhone 5?

I went into my music and tried swiping them sideways and clicking the red delete button, but the song is still there, it just has a little symbol on it that I think wants me to download it. How do I make it go away and only be the songs I want on there?
How to delete songs from my IPhone 5

Yeah. You can delete the songs on your iPhone, but to do so, you'll probably need to connect your iphone to the computer, open itunes, and delete the songs on your iphone through your computer. The "symbol" is the icloud and it's there if you want to re-download the songs onto your iphone, that you previously deleted.