"Throughout the LOTR and Hobbit series, the filmmakers have pushed the limits of the rating system, always achieving a hard PG-13 label for both the theatrical and extended versions. With Five Armies, they have for the first time crossed the limit and been given an R rating, though only for the extended edition.To be fair, my enjoyment of these films is about being in that world, and indeed it's the character moment I appreciate more than a lot of the action which is formally quite repetitious in the end. The extended BotFA received a 15-rating in the UK though and I can see why that's problematic if you're adaptating a children's novel.
"I see this as something of a betrayal of the fans, especially families, who have fallen in love with this franchise, sharing the films over many years. The reason for the R rating is probably entirely due to some extreme violence and cruelty. Certainly there is no sexual basis for such a rating, and the mild profanity mentioned above, introduced with the character of Thorin’s cousin Dain seems unlikely to have been a significant cause of the stricter rating."
Film Kristen Thompson investigates Peter Jackson's The Battle of the Five Armies, specifically the extended versions and doesn't like them as much as I do: