Joomla version 1.5.23 made a change in the SQL query used to create the starting Joomla database. This is only used when you first install a new site. The modified query uses a command that is not supported on old MySQL 3.x versions.
Because MySQL 3.x is over 8 years old, this is not likely to be an issue for most users. However, in the event that you need to install Joomla 1.5.23 on a host that does not support MySQL 4.x, here are the steps you can take:
At that point, you will be running 1.5.23.