Help with surround sound with X360 47PFL5603D/27

I'm assuming you're using component cables then. On some component cables there is an optical output like these.

http://www.bizrate.com/xboxaccessories/oid850440602.html

Then you should use an optical cable to go from the optical output on the cable to the optical input on the surround sound. This would be the best way to get the highest quality sound from your 360.

EDIT: Sorry, looks like your surround sound doesn't have an optical port, so that won't work. Since your receiver only has a digital coaxial input, and the 360 only has optical out, then you'll need one of these.

http://www.amazon.com/Digital-Optical-Toslink-Coaxial-Converter/dp/B000I98ZQY

Then it should work.