I want to get rid of some storage on my iPhone 5

I have a 16 GB iPhone 5s and I've started realizing that I need more storage on my phone. My question is that when I sync my phone to iTunes to see what I need to do to get rid of storage, it says that I have 4.59 GB that is free, but when I go to general - usage (in settings) it says that I have 1.5 GB free. I've synced my phone up multiples times to see if there was any glitch but there seems to be none whatsoever.

That is pretty unusual, I've never experience a bug like that. I could never stand 16 gig models, so I only eve got 32 gig ones instead.
I'm not sure how to resolve this particular issue, but maybe go to reseting your network settings in the settings app is worth a try.
If you have lots of pictures and videos you don't want to delete, perhaps moving them to iCloud or drop box can help you free up some memory.