Low profile buck converter
Modern buck-converters do not essentially require an electrolytic capacitor. They run on ceramic ones very good, and due the high frequency the capacictor can be smaller. The higher the frequency, the lower the capacitor value. 

For your desired project, the biggest problem will be finding a small height coil for the converter.

You have two options here

Either you use a micro-module, which are specifically designed parts that include the inductor and all components in one part and only need feedback resistors and capacitors. Usually these modules are pretty pricy, but deliver a proofen, working and optimized solution for the task, saving you all of the design procedure. Most common IC Manufacturers (Texas, Maxim, Analog Devices) have such modules in ther Portfolio. 
One example would be LTM4612 which shows a 5V, 5A solution right on top of the datasheet

The other option would be designing your own circuit. Since most convert IC's today are QFN or LGA packages, the height of the IC will not be a problem. But finding a suitable inductor could be a problem. Also it will not be an easy process to design a working and efficient design for such a high current. 
The LT8636 could to the job for the ic part, and maybe a inductor out of the XEL6030 Series could suit as a inductor