I am stunned at the nice comments on this thread. You are lucky for that.
The bike is too big for you. You have the saddle all the way down and yet since you said your legs are fully extended, there is nothing left to lower. A classic frame like this shouldn't have all that much seatpost exposed, but more than that. Based on the headtube I'd say its around a 58cm-60cm, which is too big for a 5'11" body.