Well, I like the idea of more exposure for the Nobel Peace Prize, but the question is loaded. If people name 5 generals, it is because they were famous for being generals. I bet people know 5 American Peace Prize winners, but they were famous for more than just winning the Nobel Prize:
Barack H. Obama, Peace, 2009
Al Gore, Peace, 2007
Jimmy Carter, Peace, 2002
Henry Kissinger, Peace, 1973
Woodrow Wilson, Peace, 1919
Theodore Roosevelt, Peace, 1906

I think most people would know the 5 Presidents. Most people would be surprised (and maybe dismayed) that Kissinger got the peace prize (some feel the same way about Obama). Everyone would know Martin Luther King, some Elie Wiesel. Beyond that, yes, people don't know the dozen others very well.