My Iphone wont update.

My Iphone 5s wont update. I tried updating it from my computer and every time it gets close to being finished it says,"The Iphone could not be updated. An unknown error occurred." I cant restore it because I have videos of my dog that I don't want to lose. And i never backed it up so i cant restore it anyway. Please help ive tried with two computers already and it hasn't worked. I cant even use it now because the screen only shows the cable to connect to itunes. But i cant.