It's a tough ask, and I have not found anything on Google that satisfies this. Basically, this slideshow implementation has 2 types of slides, a normal width one and a double width one. Along with that, the slider itself is wide enough so that it can have 5 normal width slides showing at once. So, this would mean that it could also have 3 normal width slides showing with 1 double width slide. The problem is that with some plugins I have tried (Slick, bxSlider), it normalizes the width of my slides on initialization, instead of keeping them at different widths. Anyone ever used a plugin that can do what I am looking for?
Try OwlCarousel: http://www.owlcarousel.owlgraphic.com/demos/autowidth.html
It supports slides with different width.