But there still have to be big moments each season, and there is no way that they will run the seasons non-chronologically like the books do. What would the big story beats be for seasons 5 and 6 if they focused solely on those two books, the "episode 9 craziness" if you will?
Season 5 could have plenty of great points in the story to end things.
-For Cersei, they could end it with her imprisonment after Season 5 has focused on her growing paranoia & mental breakdown (and fucking up the matters at King's Landing after his son & father's death). Season 6 could be about her being in prison for at least 2-3 episodes, getting to hear she gets out, then the walk of shame be a big event around the middle of the season with Season 6 ending perhaps with the fight to decide her innocence (or not). And let's not forget the Tyrells ara in King's Landing as well and how the religious faction is gaining power. Those could be BIG storylines for season 5 & 6.
-For Jon/the North, Season 5 can handle Stannis being at the wall (just showing his stuff as well has his interactions with Jon), Jon cementing his stature as the Lord Commander, scheming on saving Mance's child & sending Sam off, his interactions with Melissandre and maybe end the season maybe with them taking the wildlings in (after Season 4 ends with the attack on the wall, that would certainly be a SAY WHAT? decision for a lot of viewers that could keep them interested in the storylines of the North and bring them back for season 6 for a kind of "how in hell will that work?" hook). Then season 6 could continue with settling the wildlings in, Jon starting to meddle with the matters of the kingdom and end with the betrayal and Stannis' attack on Winterfell.
-for Dany, most of Season 5 can easily handle subjects like (as in, at least 1-2 episodes introducing the subject and then bringing them up every now and then in future episodes) dealing with the Sons of the Harpy, the prophet lady, the problems with controlling the dragons, dealing with untrustworthy advisors, dealing with the slavers and just everyday problems of an inexperienced queen running things (and yes, Daario would pop up in an episode or three). It could end with the declaration of the war by the slavers (IIRC, they declare the war before Dany accepts the proposal and that is postponed?). This end point would be very similar to how Robb's story ends in Season 1, with him being declared the King in the North and deciding to go to war with the Lannisters (just the whole KING IN THE NORTH declaration was epic as hell, you don't need all seasons to end up in epic bloodshed & war). Season 6 could have a somewhat bombastic beginning with the wedding maybe in the 2nd or 3rd episode, then Quentyn's death in the next episode and then preparations for the war and then the siege itself could be the end game of Season 6 (I've gotten the impression that the Battle of Meereen won't be too quick an affair, so it will probably happen in the span of 2-3 episodes, at least).
-for Tyrion, the first 2 episodes could focus on how low he has fallen (getting to the other side of the sea and living there for a while, getting drunk and abusing whores), then they could spend 4-5 episodes with Tyrion with Griff & Aegon (getting to know them, revealing their identity, manipulating Aegon, Tyrion almost dying) and then the last few episodes could be spent with him being caught by Jorah and then maybe end with being captured by the slavers. In season 6, he could get to Meereen quite quickly in an episode or two, for the wedding in episode 2 or 3. Then use 2-3 episodes on how he gets to Meereen, escaping the slavers. And then the rest will go with him in Meereen (or what the ever hell happens to him).
-for Theon, season 5 could be spend mostly in Winterfell and then it could perhaps end with either his escape from Winterfell or him getting to Stannis, then season 6 could continue from there.
-Martell's have to be introduced. They have plenty of story in AFFC already. We could at first be shown their mellow side, but then season 5 could end with the meaty introduction of their sinister plans for the Lannisters and introduction of Quentyn & his mission to woo Dany & get her dragons on their side.
-Greyjoys need to be given a somewhat bigger role (they'll at least have a big role in at least Dany's storyline, if ADWD is anything to go by, Martin wouldn't spend this much time with them if it wasn't somehow important).
+ there are the characters who aren't seemingly part of anything bigger atm (Arya, Sansa, Brienne, Sam) who all have their more or less lengthy storylines that will take quite a lot of time from 20 episodes even if only gone through superficially & somewhat quickly (Season 5 for Brienne could easily have the tv series show her every couple of episodes (not every episode) and then end with her being caputred & introduced to Cat, with season 6 perhaps showing a bit more than what the books have told and then her going to get Jaime and then end the season or their time in the seeries with whatever happens to both of them, taking some stuff from TWOW).
And so on and so on. There are fucktons of storylines for all characters and while not all of them have some Red Wedding level checkpoints that could end Season 5 extra dramatically, there are still plenty of dramatic stuff. Stuff like declarations of war/deciding to marry the slaver, Cersei going to prison, Jon making earthshattering decisions etc. could be plenty dramatic enough for the average watchers if they all focused on the 9th & 10th episodes. Not everything needs to have fucktons of bloodshed & war, they just need to be somewhat unexpected and/or shocking.
That is to say, it's not only doable, it's pretty much MANDATORY to use at least all of Season 5 and a lot of Season 6 for AFFC & ADWD for most characters, BUT they'll probably have to end Season 6 with stuff from TWOW for pretty much every character (more for some characters than others). Though some, like Bran, might need stuff from later on than other characters (or they could make up a lot stuff for him, perhaps explaining some of the backstory that the show is sorely missing if some of the hints at, say, Jon's parents are true & meaningful for the story, which the show has had zero mentions of).
Anyone saying otherwise has very poor memory of how much happens to everyone in AFFC & ADWD and how many characters there are altogether and how important certain storylines might be and how the show has handled the story so far (i.e. there are a lot of cuts & edits for POV characters stories, sure, but they do still touch most of the major story points for most of the characters and also add quite a lot of new scenes even for non-POV characters).