Guys,
Thanks for the answers.
Yes, the MysqlClientProvider was in the bin folder. First thing I checked...
And no, I don't need the .Net connector 5.1.3.
I use version 5.0.8.1 and it works just fine.
But thanks for the replies 
Anyway, what was wrong? I don't know. I changed a MSSQL server project to MySQL.
I think somehow VS2005 got all messed up because of the removal of several references (MSSQL) and addition of other references (MySQL).
I changed a whole lot of references, and renewed all the datasources in VS2005 and now everything works again.
But working with databinding in Winforms and changing the database certainly is a recipe for trouble... 