Carousel Picture category for each one? como? how?

I mean, my idea is that on the main page index.php carucel out a web width of all categories of my blog but these are represented by an image.

This carousel should show a 5 categories and browse the other categories by side arrows, as is typical Featured Post, but with the categories.

Know if there is a plugin that you make this?

Or in this case some advice to do so.

Thanks in advance.