The best thing about the show is that they were able to see how much a shit show skipping the 5 year gap was and were able to correct for it. This is the source of all of the problems in the books and the reason why books 4, 5, and 6 if it's every published are just shit shows of content creep/useless filler that is absolutely irrelevant and doesn't fucking matter. New temporary villains are introduced and dealt with in the in between years while all of the major characters are in 100% sleeper mode.
Arya, Bran, Samwell are all doing training montages for 5 years
Jon, Sansa and Dany are doing 1st hand lessons in leadership for 5 years
Tyrion is moping around like an emo spiderman for 5 years and finally finds purpose again.
So it's 5 years/3 books of "lets check back in on the characters you give a shit about for 30 seconds, yep still training, back to new characters nobody gives a fuck about"
He skipped the 5 year gap solely so he could tell the story of Cersei's downfall as the absolute incompetent shit leader that she is in real time instead of via flash backs.
The show realized how stupid this was and got out ahead of it:
They aged all the characters up by about 3 years at the start (the characters in the books are ~3 years younger than they were at the start of the show)
They stretched out the timelines so that each season equals roughly 1 year. Part of this is limitations of using human actors (who age, especially adolescent actors who hit puberty and who's aging you can't hide) but also it allows them to narrow down the 5 year gap.
That means at the end of Book 3 (Season 4 for the show), the characters are already 7 years older than they were in the books, and only need 1 montage season (season 5) to showcase the highlights of whats going on in the world before we enter the end game, when the characters are all now adults (or just about adults)
We're now at that end game and the show can finally continue towards the conclusion. And keep in mind, they were taking only the very best of books 4/5 for the highlight reel to make season 5. And we all remember how great season 5 was, right? Sand Snakes? and uh. yeah. The best part of Season 5, hardhome, was actually stolen out of Book 6.
Season 6 was Winds of Winter (book 6 which hasn't been released yet)
This also covers another common complaint about the TV show:
While it seems like there's a bunch of teleportation going on in the TV series (and I agree there's some questionable edits that don't allow for the semblance of large amounts of time passing) that shit is waaaay fucking worse in the books.
In the books literally like 1 year has passed. And all of the characters have done just as much traveling if not more, in less time. Well maybe 13 months now through the end of book 5.
Remember, Lolly's Stokeworth is raped during book 2 (isn't actually shown in season 2) during the protest where the high septon is killed (sansa is almost raped in this scene, but saved by the hound).
She gives birth to that rape baby half way through book fucking Four. By that time Bronn has wed her (for her father's castle) and he trolls cersei by naming the rape baby "Tyrion". There's only 1-2 more months of time that occurs after this chapter through the end of book 5.
edit: book 2 not 1.
