Not 100% sure if this is at the right section but I'll give it a shot.
I recently bought an HD 5770 card (which I absolutely love). Now I know that my card does have an HDMI outlet on my card which would obviously provide sound through the card as well. My monitor does have an HDMI input as well as speakers on it for sound. However, I use a separate 5.1 speaker setup that's connected to my board's sound output. Now, is there a way to get the HD sound output onto my 5.1 speakers if I use an HDMI cord to my monitor (currently using DVI-D) or am I just going to have to stick with what I have already? Not a big deal if I can't get it as I probably wouldn't be able to hear a major difference, but it would be nice if I could use my HDMI port instead.
your monitor would need to have an audio out, mostly found on units with built in TV tuners. In most cases the audio out would be an optical out. You would then run that to your amp but most computer 5.1 set ups have built in amps into the sub and don't accept optical cables.
So in conclusion your current set up is idle. ideal
If you had a home theater set up you could run the HDMI cable to your TV monitor from the computer. Run an optical or HDMI to your receiver and then use your HT speakers.