I cannot figure out how to update my Barotrauma to the latest edition. it is on v0.8.0.5. How do I get it on the latest edition? I can't play online otherwise

You have to open the launcher.exe from the program folder, after that you have to wait.

If it says the game is up to date, then probably just your folder says is 0.8.0.5, because the launcher does the update job automatically for you.