and when it is ready, insert the Leopard install disc.

Now restart the machine and immediately hold down the Option key. Keep it down until you see the Hard Drive and DVD icon on the desktop.
Select the DVD and allow it to boot.
SLOWLY step through the installation process until the Menu bar appears at the top of the screen.

The option you are looking for is call Utilities (or similar). Click it and choose Password Reset.
Follow the instructions from there. Change all the passwords. Remember them.

Quit the installer, reboot the Mac and test to see if you have the password correct.
If so, go ahead and do the install.
Note that the account that you will be logging into, automatically or not, will be the account of the previous owner.

BTW, the machine you purchased.......MacPro 15. Do you really mean a MacBookPro 15"
The MacPro is a tower machine and the 15 does not belong in the name.