The MySQL Site provides the installation steps. But it looks like MySQL is supported on on i5/OS V5R4 or later releases.
Currently there is a 30 day trial available and once trial period is over you will have buy the license.
Hope this helps
MySQL can be installed on V5R3 but with an older version.
Take a look to this manual :
See chapter 5. It will show you how to install an AIX version of MySQL that works fine.