On further research, it appears that HP replaced the standard lever with a push-button to eject on this model. The connector is proprietary, to the left of the SATA connector on the HP optical drive shipped with the unit.
I've left the previous information here, in case it might aid a pre-5700 model owner.
The eject button on HP Slimline PCs is a mechanical lever that presses the physical eject button on the optical drive.
If there's a cable there, it isn't for the eject button.
The cable, if it leads to that area, is most likely the power/reset/HDD light front-panel harness, but I hesitate to state that without seeing the inside of that specific model.
These end-of-life disassembly instructions may help you identify the cable.