I have already posted on several other apple forums as if your like me and have had an I phone 5 16gb and have over the past 13 months have been sending loads of pictures via text and email, when you go into settings/ general/ usage a large part of your memory is taken up in saved text messages ( I had about 3 gig) also in saved emails I had 2.5 gig both trapped in the I phone cache which you can't access.
I like most others have searched forums to find an answer to get the valued memory back I firstly found that most people found the Ibackupbot worked so I gave it ago however on the last step it kept saying that I didn't have enough space to restore my phone. The problem is that you need quite a few gig to restore your phone but when you only have 13 gig to play with when you first have your phone and then nearly 5 gig trapped it don't leave much space to play with so I found that the Ibackupbot didn't work for me as I believe that process works better with a 32 gig phone as you have loads more memory to play with.
After loads of digging I found these two techniques to get your trapped storage back.
Text cache
Before you start the process check how much memory is being used in usage on saved text messages I also synced my phone with I tunes ( not sure if it makes a difference).
1. Select Settings > General > Spotlight Search
2. Un-Check Messages in the Spotlight Search
3. Delete all text messages that show in the Messages app
4. Open the multi-tasking bar by double tapping on the Home button
5. Close ALL running applications
6. Restart your phone
Remember to reset your phone by holding the on/off button and the home button until you see the apple logo then go back in settings / general/ usage and see if the storage has reduced. ( every time I repeated the above process I noticed that a chunk of memory was given back to me it took me three times and I had freed all 3 gig.
On the third go I did delete all my current texts but a small price to pay to get 3 gig back.
To get email cache back
When I went into my sent emails even though I had deleted them all it said at the bottom there was 935 unread emails and in spot search you can still see my old emails I had sent months ago but you can't access them.
I have a hotmail account so this what I will use for my example. Basically make sure you uncheck mail and texts in spot search then delete you email account in settings/ mail.
Don't worry as all your emails you want to keep are still in the hotmail main server as your phone is only an access point to see your emails (for hotmail anyway) so reinstall your email on your phone in settings/ mail and you can upload your emails back from your inbox.
I now have 5.5 gig of space back an can install some of my apps and not worry about taking pics and videos
I hope this helps let me know if you get stuck
Cheers kurt