While it CAN be done.......be advised you'll be charged double........
IF the prospect of long run(s) of CAT5e or 6 is daunting......you might consider a Wireless-N access point and a corresponding adapter for the Slingbox....This assumes you ARE running a wireless router....????!
Just one guy's opinion......Good luck!
Another option, often overlooked by folks, for extending an in-house LAN is to use "HomePLug" or Powerline Technology. It send LAN signals over your home's powerlines so you can plug an adapter near your router and the other one at length, and it usually works....
The newer HomePLug units often use 200 Mbps sppeds between the adapters which is plenty fast for most LAN use.... I use some to get connections to the kid's XBox360s here at home, and those units are only 10 Mbps units (HomePlug v1.0) and they work fine... The kids can play games and get netflix movies with no problems.
If you are at length, definitely use Wireless .11N if you go wireless.....it has much greater distance coverages.
Split out in to its own thread topic here on this board. Click on the above link to follow it. Year old thread now closed.