So my question: what sorts of things happen in a Song of Ice and Fire (the novels, not the RPG) that you would like to see included, in one way or another, in D&D 5?
GoT is an interesting setting, and an interesting subgenre, so I think I'd capitalize on certain narrative themes.
I think one of GoT's most defining themes is
protagonist death. It's also a bit daring for D&D to try something like that -- D&D has normally been a game where one character does heroic deeds until they either succeed or die. Things like levels relate to one particular character: if that person dies, their kills, their heroism, dies with them.
To do something a little more GoT-esque, I might flirt with the idea of
lineage-as-level. That is, your "character" isn't one character, it's a family, a lineage. That is what you play as, what you control. As your family gains power and control in the world, your family gains levels. If someone wants to stop that gain of influence, they have to kill not just one hero, but your ENTIRE FAMILY. You focus in on an individual family member at any one session at the time in which they come into conflict with the other families.
If that family member loses that conflict, then your character -- your family -- suffers under some penalty. A "death spiral" comes into effect, where one failure is more likely to produce more failures, though each generation is a chance to reverse that trend.
My first choice is easily mortality rates. Characters in SoIaF don't hack their way through hordes of orcs. They hesitate even to begin a fight, because fights mean death. I'd like to see D&D 5 make characters more fragile, and put greater emphasis on social and intellectual conflict than on physical conflict.
I think where you lose me is the idea that 5e more broadly should to be more GoT-esque -- I'm not sure I agree with that. D&D is not the same kind of experience that the novels or the TV shows are. They can be different things, just as D&D and LotR, or D&D and Harry Potter are different things.
I'm a fan of modules, though. And I think a "more lethal" HP module where you can die in one hit is a likely candidate for 5e. I'm not sure I think that 5e needs to make characters more fragile or put more emphasis on social and intellectual conflict, period, but I'd like the ability to take it in that direction if I'm in that mood for a night or a campaign or whatever.
All D&D needs to do as a default is give a good dungeon crawl, I think, and there's not much you can learn from GoT's style in regards to crawling a dungeon. But D&D can be more than that, too, and so there's good ideas to take if you want more than that.