Help with part and/or circuit 3-15V input, 5V output power supply - Boost, buck, SEPIC,?
I'd suggest the LM3488 current mode controller in a SEPIC configuration.

It utilizes an external FET switch so provided your support components are selected with suitable ratings then you can supply as much current as you like if your source is up to it.

I've used this particular part for a 6A/24V SEPIC converter from a 10-30V battery (Car/Truck) voltage input range.

There are many applications notes and design guides for this part.