*** SPOILERS TO FOLLOW ***
The theme that really struck me was redemption. It was so prominent to me there that were two characters in whom this theme showed its mark. One I think is pretty obvious to all who would see the movie. This would be in Thorin Oakenshield.
He was well on his way to becoming a villain in this story as he and his fellow dwarves retook the treasures of Erebor. His predictable fall into the dragon sickness of the riches that drove his grandfather mad was maddening to watch. It was so powerful in its hold on him that he was ready to let his cousin Dain die on the battlefield without help and he even threatened to slay Dwalin and Bilbo.
Yet at the moment when it seemed the dwarves were going to succumb to the armies of the orcs Thorin had his moment of redemption. He was in the golden hall which featured prominently at the end of Desolation of Smaug and with voices running through his head his eyes were finally opened. He didn't want to fall into madness like his grandfather Thror had, and he finally heard the wisdom of his friends. Thorin immediately turned to the path of redemption. He rejoined the other twelve and they led Dain and his army in a rally against the orcs.
In the end, Thorin after having slain Azog and also been dealt a death blow of his own has one final conversation with Bilbo apologizing for all that he had put him through. Thorin was over his love of gold and back to his love of friend and family.
There is Another
The other story of redemption is not nearly as noticeable. I didn't think much of it my first viewing but it really caught me the second time around. This one involves Thranduil. He too, like Thorin, was going down a dark path. He too, was nearly becoming a villain. His lack of love for those outside his kingdom came to the forefront in Desolation of Smaug and Tauriel confronted him on it. In Battle of the Five Armies we see a glimmer of hope when he arrives in Dale with food and supplies for the remnant of Lake Town. Though he seems to dash that hope when he notes for Bard that he isn't there to save them, he's there for his gems in Erebor.
Thranduil and Tauriel have another run-in in B.O.T.F.A. when in the midst of battle Thranduil prepares to take his elven army back home and Tauriel tries to stop him. He speaks down on her for her relationship with Kili the dwarf and says her love is not real.
It was that last comment that caught me this second time around. For at the end of the film he meets again with Tauriel at the end of battle. Tauriel is sitting next to the slain body of Kili crying and heartbroken. She looks up at Thranduil and says "why does it hurt so much?" Thranduil there has his moment of redemption. You can see his heart soften to the plight of Tauriel. He is likely considering the loss of his own wife which Legolas had mentioned earlier in the film. Thranduil replies to Tauriel "it hurts because it is real [her love]." Though the film doesn't really show us where this pair goes from there it can be seen that Thranduil may have redeemed and softened his heart.
One other note that caught me in seeing BOTFA again was the wonderful job Peter Jackson once again did with his Tolkien-esque portrayal of the hobbits. In contrast to the gold-loving dragon-sickness of Thorin, and the cold heartless demeanor of Thorin is Bilbo Baggins of the Shire. There is a scene where Thorin comes upon Bilbo fumbling with something in his hands. Of course the viewer is meant to think Bilbo is playing with the arkenstone and Thorin will discover this and blow his top. Instead, Bilbo has an acorn.