I feel like this question would benefit from a spoiler-free overview, by character. The final section details which book characters don't appear in the TV show and visa versa, so stop reading before that heading if you don't want to know. Where the TV show contains possible spoilers for unwritten books, I've put the episode numbers where these occur in spoiler tags so they are easier to avoid.
First, overall, Season 5 is where Game Of Thrones starts to really diverge from the books. Before Season 4, the main plots are similar enough that a book reader could start watching the show at Season 4 and have little trouble understanding what's going on. Things started to diverge irreversibly in Season 4, then in Season 5 these develop into major multi-season plot lines that only exist in the TV show and replace some major multi-book plots. Arguably, and probably not coincidentally, the writing becomes sporadically less tight in terms of characterisation, dialogue and consistency (some fans wonder if the writing team changed) - but let's not get into that here.
Spoiler-free (books and show) plot changes by character, from least-changed to most-changed:
Somewhat similar storylines
- Arya. While many details are different, including which previously-named characters she encounters, the general direction and tone is very similar. The books go further than the show, continuing along similar lines.
- Cersei. Massively simplified in the TV show, with very few new characters introduced (compared to many, many new characters in the books). Cersei is also portrayed slightly differently (a little stronger and arguably saner in the TV show, certainly not quite as risk-taking, erratic, inconsistently trusting or... predatory as she is in the books), but the overall storylines have a similar general gist and tone.
Sam's storyline doesn't go nearly as far in the TV show as the books, but it looks to be heading in a similar direction - with some added drama that doesn't feature in the books but fits the theme and his situation. The books contain a "journey of discovery" theme storyline not (yet?) in the TV show. In seasons 6 and 7:
Sam's story takes some show-only twists and skips much of the book's journeying, but converges to end up in a similar-looking spot.
Some very big changes
- Jon. Begins quite similar (but simplified and accelerated in the TV show). His storyline then takes a dramatic turn that is very different to the books and depicts things not (yet?) seen in the books. Jon's story in the books is intensely political, while in the TV show, there's much more action. It's hard to say more without dropping massive spoilers... but it's possible the book and TV storylines might converge in future works.
Stannis. There are some big differences around which characters in Stannis's company go where, and the TV show spends much more time with Stannis directly - most of the equivalent events happen off-stage in the books, which means the TV show appears to answer some questions which are left unknown in the books (containing possible Winds of Winter spoilers). There are some major, very dramatic scenes and plot points added to the TV show that can't happen in the book world, but which could be spoiler-y clues as to events that may happen, or turn out to have happened, under different circumstances. If book readers want to avoid these episodes, they occur in episodes numbered:
9 and 10, following lots of foreshadowing particularly in episode 6. Episode 10 is the most spoiler-y.
Dany. Similar gist, but almost all the details are different. While the TV show dips slightly into political themes around the difficulties of ruling a city, the books go into much more rich details about the economic situation, precise relationships with regional neighbours, factional politics, etc etc. Her personality continues to be somewhat different - more stern and decisive in the TV show, more naive and reliant on advisors in the books (partly due to her being younger in the books). Very few new characters are introduced in the TV show, compared to many in the books, but some dramatic scenes are added.
Tyrion. In the TV show his journey is massively simplified and shortened, with very few new characters introduced and different character(s) accompanying him. In the books his storyline is much more meandering and much less linear. The TV show then features events which haven't happened in the books, can't happen how they do here in the book world, but could be clues as to where Tyrion's story will go. Therefore, there are possible spoiler-y clues about where Tyrion might be going in Winds of Winter, in episodes numbered...
6 and onwards, and all of seasons 6 and 7
- Littlefinger. He's still scheming in both, but his schemes are very different, in different locations. The TV show spends more time with him than the books.
- Jorah. Starts somewhat similar, takes a very different twist in the TV show. Is slightly more central in the TV show than the books.
- Theon & the Boltons. Similar predicament and some events in common, but most of the details are extremely different. Similar characterization, although Ramsay, as with earlier seasons, arguably shows more strategic savvy and self-control in the TV show than his often crude knee-jerk bullying in the books, and his relationship with Roose is more developed in the TV show than the books which focus more on his relationship with his younger peers (but he is just as sadistic, savage and shocking in both)
- Doran Martell and some associated Dornish characters have a storyline that has a few very slight similarities between the books and TV show in terms of main characters' rough intentions, but the content, tone and style are completely different. Whereas in the books, it's based around many interweaving political plots and mysteries, in the TV show it's simplified to the point of barely being a storyline (quite one-dimensional and shallow, but dramatic in places).
- Varys. Takes over the storylines of a few characters who don't feature in the TV show. He starts in a similar place but goes somewhere very different, literally and figuratively.
- Sansa. Has a much, much bigger and more dramatic role in the TV show. In the books, she features little, but in the TV show, hers is one of the most central plot lines of the season.
- Jaime. Has completely different storylines in the show and books, in content, location, company, and tone. His TV show storyline is somewhat cartoonish and action-oriented, while his book storyline is more based around character development towards leadership and strategy.
- Brienne. Her storyline had already diverged last season, and continues to take a completely different course. Her story has more drama and is more closely integrated with other characters in the TV show, but has less personal character development and much less walking around compared to her storyline in the books.
- Davos. He plays a smaller, supporting role to other character(s) in the TV show, completely unlike his adventure in the books.
- Jaqen arguably appears in both, but in ways which are different in every possible way. Or perhaps he doesn't appear in either? Both Jaqen H'ghar storylines, if they are Jaqen H'ghar storylines, have only one thing in common, and that's mysteriousness.
After this are changes in which characters appear at all.
You might want to stop reading if you consider this a spoiler - but no particular plot points are given away.
Not featured in the TV show
- The iron islanders have three interwoven storylines in the books that don't feature in the TV show, with a mix of politics, action, adventure and... disturbing moments. There's nothing to rule out some of the new characters here appearing in season 6.
- Quentin Martell, a son of Doran, appears in the books and has an adventure-themed storyline that appears to have been dropped completely from the TV show.
- Arienne Martell, a daughter of Doran, appears in the books and has an intrigue and mystery themed storyline that appears to have been dropped completely from the TV show except for a few elements merged into the Doran et al story.
- Griff and company are introduced in the books and have a complex storyline that doesn't appear in the show (but, unlike the above Martells, isn't necessarily ruled out from appearing in a later series under different circumstances)
- Pate, a hapless wannabe maester, and some acolytes and maesters in the Citadel are introduced in the books but not the show, in storylines that introduce new mysteries
- Bran and company don't appear this season, while in the books their storyline continues very slightly further and, arguably, he is seen using his new abilities to influence other events
- Varamyr, a wildling warg/skinchanger, appears in the books and has a mysterious, dark high-fantasy storyline, which doesn't have any equivalent in the show
- The brotherhood without banners return in the books with a chilling new leader. In the TV show, that new leader isn't introduced and they don't feature this season
In seasons 6 and 7:
Euron and Aeron Greyjoy appear, and the brotherhood without banners return, with storylines that are fairly different and dialled down compared to the books
Not featured in the books
- Bronn is talked about and causes some mischief in the books, but doesn't appear directly, whereas in the TV show he joins another character's storyline in a more prominent role
- Karsi, a female wildling leader, is introduced late on in the TV show only (played by Birgitte Hjort Sørensen, who played Borgen's Katrine Fønsmark), as a strong character with some excellent lines, in a political storyline that doesn't really have an equivalent in the books.
- The white walkers / others don't appear directly in the books this season is loosely based on. TV show contains possible small Winds of Winter spoilers around the attributes and organisation of White Walkers / others (assuming that the TV show's white walkers aren't differently imagined to the books' Others, which is possible), in episodes numbered...
- Hardhome and the wildlings sheltering there are only referred to indirectly in the books, but shown directly in the TV show. The events are different enough that this can't realistically be considered a spoiler for future books.
I think that covers all the major characters whose stories aren't at this point arguably covered by another character's story