Storage problem on iPhone 5s?

I've only had the phone for 3 months. It's been out of data for a while. I only have 5 apps, NO music, NO photos, NO video. I calculated megabytes into gigabytes & with the 5 apps I have, it ONLY adds up to 510MB. Which is ridiculous, because my phone says that 13GB have been used up. What should I do? I can't restore the stupid phone because my mom out the restrictions code in & doesn't remember it. ITunes won't allow me to use my phone with it because I need the newest version (11.1) WHICH I DO HAVE. I seriously need help. This is ridiculous.

On the phone, go to Settings, then General, then Usage. It will show what is using your storage. It could be one of your apps, or it could be email. Free up the space used by the culprit.

This isn't a fix for the problem. Deleted all huge aps and still says ZERO available. What's the real solution?

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