I'll stick my neck out: due to the influence of mobile and web apps the file system and explorer as we know it will have disappeared in 5 years to be replaced with something better.
Some day, there will be enough computing power and storage in a tiny device and we'll just have different size screens. But that's a ways off.
The desktop is not at all dead if the alternative is only reaching pad and smartphone users. Not even close to mortally wounded for business or home. My kid's school switched them to iPads and they immediately identified the problem--they hate typing on the things. My son takes paper notes. They're fine for consuming, but that's it.
Then there is the problem of app discovery, not to mention the pricing and business models that exists in the mobile world. They pretty much limit success to the few at the top with a lot of sharecroppers scratching out a living down below. It's even bad enough that Fred Wilson backed off a tad from the mobile first mantra.
More here: http://smoothspan.wordpress.com/2012/10/15/mobile-first-for-...
If by mobile first you mean smartphones and tablets, absolutely not, these don't have enough processing power to replace desktops unless all you do is email some docs and web, anything intensive (IDE, virtualization, image/video editing, vector design, 3d, and the list goes on) will require at least a laptop. Also most PC gamers will keep on going with the desktops not even laptops (I'm more a casual gamer now but the games I run don't even exist for any tablet, and most laptops will have to run them in low settings)
It has nothing to do with which device is more important or more common.
This used to be a required demographic to have endorse ones computer product, but no longer. Most users just want to do stuff and don't care about technology.
I expect the desktop will remain, if only as a convenient horizontal surface on which to place a keyboard and one or more displays. It won't matter where the computation takes place.
It depends on what you are trying to accomplish. A smartphone is great to tweet, etc. But you wouldn't want to Photoshop a poster with it. There are just so many shades of grey between those two extremes and it all depends on the use case you are specifying.