The only reason of not dropping price below 5000 usd is that mining won't be profitable.
That's not the "only" reason, but a very strong one. The reason #1 is the one I posted.
This is a very weak argument really. No one gives a fuck about mining costs, let alone there being a single cost of mining in the first place. If anything, whatever bitcoin price might be (5k or 1k), there will always be enough miners as mining will always stay profitable at any price. If mining is no longer profitable for some miners, they just leave while the rest picks up the slack instantly taking their share of the reward pie (as the reward remains the same). No offense intended, but honestly, when people bring up this argument about costs of mining, you can be certain that they don't have a clue about how everything works regarding prices, costs, and other economic matters.
As to your claim in the OP, anyone with enough bitcoins (like the mtgox dude) can crash the price to 1k or even below and keep it there as long as he sees fit. There is no reason to prove you wrong as it is just a matter of someone with deep enough pockets, for example, Satoshi and his likes, choosing to dump enough coins. There is nothing to prove here.
No - it is important because people who are heavily involved in mining who happens to have a considerable wealth, will always try to manipulate the price above their profitability rate.
Manipulating up a 100B$ market is easier than manipulating it down.
Simple as that, if you disagree read again because it's a very simple concept.