It would be easier if you told which card that is, but luckily I saw the necessary info from that pic even its blurry. I think that card is Nvidia 8500 GT made by Asus. Correct? I found two answers and they are:
1. Sound cable for HDMI (that you can carry sound and video over HDMI)
2. Power cable for fan.
My guess is that its not power cable but sound cable for HDMI cos those old cards usually dont have external power cables even for fans. Fan can have shorter cable connected straight to graphic card.
EDIT: You can google: "asus 8500 gt wire" if you want to read those forums more
