how can I delete a song from iphone 5

Quick Fix: Go to Settings -> General -> Spotlight Search -> uncheck songs and then press the Home button. This should disable all messages from appearing in the search.

Guaranteed Fix: Go to Settings -> General -> Reset -> Erase All Content and Settings. This will erase everything on the phone. This is the only way to "clear" the search results.

To delete songs from iPhone permanently,you can use a iPhone data eraser.
iPhone data eraser tool can easily wipe, erase, deleted data from iPhone,the ios data eraser supports erase iPhone text messages, contacts, photos, videos, account info, password and other personal stuff. iPhone Data Eraser is such a tool to perform a permanent data erasing on your iPhone.

For a simple delete, just go to the desired songs' album and swipe your finger from right to left over the song title. Now tap Delete!

Your response really confuses me. By the way, I'm not sure I'd trust that third-party software in the link...