How to get 5v 2a from low voltage, high amperage solar panels
A DC/DC boost converter seems like a good solution to me. The closer to 5V your input is, the more efficient it will be and the more current you will be able to get out of it.

You see a lot of 500mA because that's the USB standard.

There are beefier converter out there, going all the way down to an input voltage of 1V. You could also design your own using TI's tool: webbench (I like using it as a starting point in my designs). But it probably makes sense to buy one off the shelf. 

Searching for "dc dc boost 1V to 5V 2A" gave me one hit on bangood for 0.99USD ... There are other, more expensive and more reputable around.