There's only one indication in The Battle of the Five Armies that Saruman was going Dark Side, and it only works as one if you've also seen The Fellowship of the Ring. After Galadriel unleashes the Light of Eärendil on Sauron and the Nine, Sarumen gets this really bad-ass oneliner:
Saruman: Leave Sauron to me.
The Hobbit: The Battle of the Five Armies (2014)
Which sounds amazing, but if you've seen Fellowship then you know that Saruman did a spectacularly bad job of dealing with Sauron.
Of course this is far from conclusive evidence, but that's kind of the point. If it was easy to point to evidence of Saruman going Bad, it wouldn't have taken until Fellowship for anyone to have figured it out.
A better indicator, although one that suffers the same problem, comes from An Unexpected Journey during the meeting scene in Rivendell. Despite word-of-mouth evidence from two wizards, whom Saruman should have no good reason to distrust, and eventually a dagger that should not exist, Saruman continues to deny the possibility of Sauron's return. Even without the benefit of hindsight, this evidence should have been enough to at least warrant investigation. Once again this isn't exactly evidence that Saruman has ulterior motives, but it's a move that really only makes sense once you know that he does.
In the books, Saruman is unquestionably looking for the One Ring independently of the White Council by this time:
2850 Gandalf again enters Dol Guldur, and discovers that its master is indeed Sauron, who is gathering all the Rings and seeking for news of the One, and of Isildur's Heir. He finds Thráin and receives the key of Erebor. Thráin dies in Dol Guldur.
2851 The White Council meets. Gandalf urges an attack on Dol Guldur. Saruman overrules him.
Return of the King Appendix B: "The Third Age (ii) The Third Age
In-text, there's a footnote on that last entry:
It afterwards became clear that Saruman had then begun to desire to possess the One Ring himself, and he hoped it might reveal itself, seeking its master, if Sauron were let be for a time.
Return of the King Appendix B: "The Third Age (ii) The Third Age
Just to complete the chronology, the Quest for Erebor takes place about a hundred years later:
2941 Thorin Oakenshield and Gandalf visit Bilbo in the Shire. Bilbo meets Sméagol-Gollum and finds the Ring. The White Council meets; Saruman agrees to an attack on Dol Guldur, since he now wishes to prevent Sauron from searching the River1. Sauron having made his plans abandons Dol Guldur. The Battle of the Five Armies in Dale.2
Return of the King Appendix B: "The Third Age (ii) The Third Age
1 The River Anduin, where Isildur was killed and the Ring lost
2 I'm putting the rest of the entry in spoiler tags, for anyone who hasn't seen the movie or read the book:
Death of Thorin II. Bard of Esgaroth slays Smaug. Dáin of the Iron Hills becomes King under the Mountain (Dáin II).