Ok, well there is no question that the 5600 supports speakerphone on the talk key. I would hazzard a guess that SpeakerPhone isn't working becuase of it being stuck on headset.
My guess as to why it won't come off headset is that you might have some dirt or lint stuck in the jack. Try blowing into the jack, or maybe use a can of compressed air. Also repeatedly inserting and removing the headset should loosen whatever it is and allow it to toggle back.
Let us know how it goes.
"I have no special talents, I am only passionately curious" - Albert Einstein