5S will not restore, iTunes says not enough memory.

I just backed up my iPhone 5s last week on my computer. Last night, my contacts dissappeared. My cat was laying on it and it was open to Mail, Contacts ......

I doubt he did it as I have been having problems with some of the contacts dissappearing lately anyways.

I first noticed that my iMessages just had phone numbers to identify them, and then I noticed my contacts are gone.

I attempted to restore my phone from my last back up and I continue to get the error that there isn't enough memory on my phone to restore.

I have 3.3gb available.....

BTW - I have already reinstalled iTunes, rebooted my phone, deleted large files... etc.....

Thank you for any suggestions.