I don't know if every 5 or 6 year old child does this, but I'm sure a good few do. I have 6 kids, 8yrs-2yrs. My 8 year old is the worlds WORST when it comes to things like this. And he still does it. However my 7 year old daughter, my 6 year old son, and 5 year old daughter and on down...well, they don't do that.
I chalk it up to mostly personality. While my other kids have learned to shake hands and say (and mean it) "Good Game", even if they do lose..my 8yr old just get's upset.
What do I do? Reinforce to him that not everyone can win and that the point to a game,even in sports, is to have fun. That sometimes you may win and sometimes you may not. Now, does this always work? No, but that is his personality. He is that way with everything in his life. His school work has to be perfect, he has to read more than any other kid, be finished first with his work and his work has to be perfect. That's just his personality. And I have learned that when we are playing a game, and I can see that he is starting to get aggitated, then I say "You're done, you need to leave the table because that is not how you act." Then he sees everyone else still having fun and realizes that he can't act that way.
My 8 year old isn't as bad as he was when he was a little youger, but it's a learning process and I hope that he continue to learns.
Best of Luck!