Well let's see...
S5 is larger, weighs less, has a better resolution, has better pixel density, screen is better, has a larger camera, the camcorder is 4K, system chip and processor is faster, better battery, and you can pick it up for as cheap as $99 on contract.
Fire Phone is tied perfectly into their own ecosystem (ala Apple), has Dynamic Perspective (3D it's not).
Based on specs I don't see it as being a better phone. S5 is one of the best phones out there, IMHO. Amazon comes in close to the iPhone 5S instead of the Samsung S5.