Will iTunes Match back up music that's not in iTunes but on my iPhone 5?

Hi,

No. The music needs to be in your iTunes library on your computer. You will need to get an app that let's you transfer music to your computer.

Jim

No but it will shut down your phone if you toggle the Itunes match switch in settings.

<Edited by Host>

lelebelle wrote:

Do you know of any apps that will back up my music?

See these user tips for getting your music from your iOS device to your iTunes library:

Recovering your iTunes library from your iPod or iOS device

Syncing to a "New" Computer or replacing a "crashed" Hard Drive

For backing up your personal data, if you are using OS X Time Machine is built right into the OS. All you have to do is plug in an external USB HDD, enable it and forget it (not literally forget it, but it works automatically in the background). If you're using Windows you'll need to do some research to find backup software.