In order to play in a tournament I have to play five online chess games, so I played five or six blitz games, only to learn that they don't count. I'm guessing that means all live chess games don't count and only five correspondence games do?
Yeah, that's because toournamnets are correspondence. You have to show that you are here to stay. :)
I have five completed correspondence games and it still isn't letting me join a tournament. One of the completed games was an unrated game that was played by a Chess.com volunteer. Could that game not count?
It looks like they don't count your greeter game towards that total. Your statistics show 4 completed games, so 1 more should do the trick unless the specific tournament you're trying to join has a different requirement listed.
You should also keep in mind that many user-organised tournaments have higher requirements. The main goal is to make sure your rating is stable; it often happens that someone who is capable of (say) a rating of 2000 is only at 1400 after 5 games or so. If he then joins a tourney with a 1400-1600 rating range, the players who are really of that level will be eaten alive.
When using brackets I usually go for 20 completed games as a minimum.
You should also keep in mind that many user-organised tournaments have higher requirements. The main goal is to make sure your rating is stable; it often happens that someone who is capable of (say) a rating of 2000 is only at 1400 after 5 games or so. If he then joins a tourney with a 1400-1600 rating range, the players who are really of that level will be eaten alive.
When using brackets I usually go for 20 completed games as a minimum.
Yeah, I noticed the Turtle tourney required 10. 
I can see your point regarding the rating score. Mine is way higher then it should be. I won two games due to my opponent losing their queen accidentally early in the game. One was on turn 8, which he promptly resigned. While I like my rating, I know it isn't correct and should be lower. I'm guessing mine will level off around the mid 1300's to upper 1400's.
In order to play in a tournament I have to play five online chess games, so I played five or six blitz games, only to learn that they don't count. I'm guessing that means all live chess games don't count and only five correspondence games do?