In most cases, the television show has already reached the point where the most recent novel (A Dance with Dragons) has left off; the finale on Season 5 lines up pretty cleanly with the end of that novel. (In some cases, like Bran, the show ran out of story last season).
In other cases, the show has deviated quite a bit from the novels, especially with Sansa, Arya, and Tyrion.
In either case, it's been made pretty clear at this point that the producers on the show are going to need to diverge from the novels from this point forward.
While I strongly recommend you read the books, starting with A Game of Thrones and in order, you aren't going to find anything "beyond" the TV Show in them. It will fill in some extra details, especially about the backstory of some of the characters. In addition, Martin is currently writing the next book, Winds of Winter, which he plans to release "before Season 6". However, I'm not sure how much of what going into the books from here on out will really come into play in the show.
In short: you should read the books because they're good books and you'll probably enjoy them. Just don't read them expecting to "get a head start" on the show, or you may be disappointed.