The S5L8720 is the processor used in the iPod touch (2nd generation). It runs at 533 MHz.
The S5L8720 is one of the few iDevice processors to have an untethered bootrom exploit; The advantage of a bootrom level exploit is the ability to jailbreak any device utilizing the processor, regardless of the version of iPhone OS/iOS installed. By having an untethered bootrom level exploit, a computer is not needed to assist in booting the device.
There are two known exploits for the S5L8720: 24kPwn (0x24000 Segment Overflow) (untethered; old bootrom only) and
usb_control_msg(0xA1, 1) (tethered; both bootroms).
The S5L8720 is one of two processors to have two different bootroms; The other being the S5L8920. Roughly seven months after the release of the 24kPwn (0x24000 Segment Overflow), Apple released updated iPod touch (2nd generation) devices containing a newer bootrom that was no longer vulnerable; This closed the hole that allowed an untethered bootrom level exploit.
Later, a new exploit,
usb_control_msg(0xA1, 1) (sometimes referred to as "steaks4uce") was discovered. This exploit, when combined with a kernel exploit, allows a tethered jailbreak on newer bootroms.