Did you want to erase your hard drive completely clean?
Yes, boot the Mini with the 10.5 (<--) Install disk. When the first of the install windows appears, go to the menu bar and find 'Disk Utility', might be under Utilities or Applications.
Once that opens, the program has a list of drives on the left, select the one that is the Mac Mini's internal drive. Make sure you select one that is left aligned/has the size of the disk and the brand. Then on the right side choose the 'Erase' tab. The volume format should be 'Mac OS Extended (Journaled)'. Then click on the 'Security Options' button near the bottom. Choose zero-out data for the simplest secure erase (it does this by writing 0's all over the disk).
The click OK, and Erase.