I've read both a few of the negotiation books (Getting to yes, Getting past no) and Five Dysfunctions and I don't know that I'd recommend them, to be honest.

My beef with Five Dysfunctions is primarily the book recommending MBTI. MBTI has the predictive value of horoscopes, more or less. Really hard to take anything said seriously at that point.

The negotiation-series has some value, and has helped me succeed in some negotiations, but I'd honestly recommend Never split the difference as a substitute. Having read that book instead would probably have saved me more than a few poor outcomes in negotiations.

Finally I'd like to recommend Peopleware - surely one of - if not the definitively - best book I've read for professional purposes.