Installing MySQL 5 Server on Ubuntu is a quick and easy process. It almost feels like it should be more difficult.
Open a terminal window, and use the following command:
sudo apt-get install mysql-server
If you are running PHP you will also need to install the php module for mysql 5:
sudo apt-get install php5-mysql
To create a new database, use the mysqladmin command:
mysqladmin create <databasename>
See, really easy!