I understand that you want to know if you can connect the Slingbox PRO to your cable box using the HDMI cable.
The short answer is no. But first, I'd like to clarify some details. The port you find on the Slingbox PRO back panel is not for the HDMI cable. It is for the HD Connect cable. Having said this, you must also know that none of the Slingbox models will work with the HDMI cable since they are not compatible due to the High-Bandwidth Digital Content Protection (HDCP) restrictions.
The following link will provide you with further details about this specific situation:
I get no video with any SlingPlayer (Watch, Windows, or Mac OS)
Since the Slingbox PRO does not have Component inputs (RGB), you must use the Composite cable (yellow for video) and the red and white cables for audio. As a second option, you can use the HD Connect cable, however, you'll need to track it down through the Internet since it has been discontinued.
Finally, you can use the Airport Express if you want to connect the Slingbox to your router. Futher details are included here:
Hope this helps!