in The Hobbit: The Battle of the Five Armies. after Galadriel, Elrond and Saruman rescue Gandalf and banished the formless Sauron they encountered Saruman proceeded to go after Sauron alone

Galadriel: The spirit of Sauron endured.
Saruman: And has been banished.
Galadriel: He will flee into the east.
Elrond: Gondor should be warned. They must set a watch on the walls of Mordor.
Saruman: No. Look after the Lady Galadriel. She has spent much of her power. Her strength is failing. Take her to Lothlórien.
Elrond: My Lord Saruman, he must be hunted down and destroyed, once and for all. Saruman: Without the Ring of Power, Sauron can never again hold dominion over Middle-earth. Go now! Leave Sauron to me.

many years later Gandalf learned that Saruman has turn traitor and has sided with Sauron. i am wondering, was Saruman already siding with Sauron when he and the others came to Dol Guldur? suggesting Elrond to look after Galadriel as opposed to letting Elrond warn Gondor as an act to protect Sauron?

  • The accepted answer in the linked question states the point where Saruman had begun his dark thoughts, and was already trying to find the One Ring for himself before Dol Guldur. Any answer to your "more specific" question would be an almost identical duplicate of the answer above.
    – Edlothiad
    Commented Feb 13, 2018 at 6:43
  • Forgot to say +1 for the good question, it was unfortunately already asked but is very interesting none-the-less!
    – Edlothiad
    Commented Feb 13, 2018 at 7:58