Cleaning up a rotating image gallery
For the css part, I started from the updated fiddle @cimmanon provided. I basically agree with all the things he added. I also went ahead and turned your markup into a ul as he (or she) correctly suggested. I would like to provide my own insights as well:


You are closing your img tags, however they can never contain any content so the closing tags are redundant (and perhaps even invalid). You can either make them self-closing (&lt;img ... /&gt;) or just omit them in html5.
You are using a lot of different classes in your markup. There is no real need for that; all it does is make your code longer and harder to read. I would go for selectors like .image-gallery img instead of .gallery_image. I admit that in theory this is slightly less performant, but I doubt you'll be able to see, or even measure, the difference. And it makes your markup a lot easier to maintain (less code when adding slides, and less chance of making typos in all those class names).
I would definitely not animate the left property, but go for a transform: translate3d in stead. It is a lot better for performance as explained here.
I would use css transitions, instead of the jQuery animate. It is again better for performance, and it I believe it makes your code a lot better structured. If you decide to change anything in your animation, you just have to update your css and you don't have to start digging into your javascript. I'm a big fan of only using Javascript for thing that can't be done through css.


I went ahead and applied my suggestions to the fiddle, which you can find here: http://jsfiddle.net/eL0vaL44/3/