Question: If so where can I find the installation?

Answer: 
It's not installed by default in Mac OS X 10.5. You can install it via a package manager like MacPorts, or from the package on the [MySQL web site](http://dev.mysql.com/doc/refman/5.0/en/mac-os-x-installation.html).
As a side note: when using Time Machine you may be interested in excluding the log files, which by default are hidden in a directory that even an admin account cannot access:

```
ls -la /usr/local/mysql-5.0.51a-osx10.5-x86
[..]
drwxr-x---   4 _mysql  wheel    136 Jul 10 23:06 data
[..]
```

Or, change the MySQL settings to move the logs to some temp folder.

(To remove existing MySQL log files from the backup disk, you need to [run Time Machine as root](https://superuser.com/questions/35152/how-do-i-retrieve-files-from-time-machine-backups-from-another-computer/35309#35309).)