Iphone 5s says storage is full when I have few images/videos or apps on it
Have you checked your "Recently deleted" album? Maybe it takes up your storage. Since iOS 8, the pics and videos you deleted are not actually gone. If you want to make them disappeared you need to go to the "Recently deleted" album and delete them again. Otherwise you need to wait for 30 days they will be deleted automatically. You should check it.

There are just too many things that require physical storage. That's why Apple chose to lump a lot of things into the "Other" category. it's seems like your phone is filled with cached files and data. That can include:


Documents &amp; Data
Safari browsing data
Mail data
iTunes data, including files that have been streamed (which can be
BIG)...


Since iTunes categorizes cached files as Other, reported usage for Music or Videos might differ.

Deleting data, and then restoring is a good way, but you should back up first. or it will cause data lost. 

In addition, you can try to clean up cache files frequently. This thread is for your reference.