Need help recovering root password in Ubuntu

Like any good Linux system, my Ubuntu 5.10-installed laptop protects root access with a password. Unfortunately, I have no idea what this password is, and I’m certain I wasn’t prompted to specify it during install. I can obtian root access by interrupting GRUB during the boot process and booting into Recovery Mode. This automatically logs me in as root, without requesting a password. I’d like to find the root password so I don’t have to reboot anytime I need root permissions. Any idea how I can find my root password?