The volume up button on my iphone5s won't work? The down button works fine, but the up one just dosen't work at all. Is my phone broke or is it just the button that's broke?

Most likely it's just the button that is broken. I wouldn't recommend trying to fix it yourself, though. Take it to your carrier or talk to your phone insurance (if you have it) and see what they can do to help you out. Perhaps this is a sign to upgrade to the iPhone 6! :)