Bluehost MySQL database
Websites hosted at Bluehost are offered with two versions of MySQL database management services - MySQL 4 Servers and MySQL 5 Servers.

As a Bluehost customers, you’re offered with the choice between these two MySQL versions, but never both. For ReviewBluehost.com for example, the MySQL version is MySQL 5.0.45 Version.
To check the MySQL version of your account, all you need to do is login into your hosting control panel page, scroll down and look for the “MySQL version” on the right column.
Refer figure for the MySQL version at my hosting account.
What’s MySQL?
MySQL is an extremely popular “relational database management system (RDBMS)” which has more than 11 million installations according to the officials.
In fact, MySQL has become the #1 database choice for delivering web applications, where the program powers high profile web sites such as Yahoo!, Google, Flickr, YouTube, Wikipedia and millions of websites running on Apache servers.

MySQL is such popular mainly because of the program infrastructure implementation are highly leveraging the popular open source LAMP stack (Linux, Apache, MySQL, PHP/Perl/Python).
The program runs as a server providing multi-user access to a number of databases. MySQL is owned and sponsored by a single for-profit firm, the Swedish company MySQL AB, now a subsidiary of Sun Microsystems, which holds the copyright to most of the codebase.