You would most likely need to connect your HDMI PC output into a audio receiver of some type that is able to relay the video to the tv/monitor. This would allow the audio receiver to do the audio magic, while passing the video to the display of your choice. If you are simply sending HDMI audio/video to a standard HDTV that only has on board stereo speakers, don't expect 5.1 to appear magically.
However, my Sony Bravia (HDTV) is able to send the audio through optically to my receiver from a HDMI input from my PC to my audio receiver, which from all the tests I've tried, seems to work just fine.
Really though, you could find some dual pin (stereo) input to triple pin (3 way) output 3.5mm headphone converters somewhere. This would allow you to use 5.1 on your 3 connections on your motherboard. Much cheaper than a "real" sound card.
If your serious about audio, get a sound card. Creative labs has good gaming sound cards. I really enjoy my Asus Xonar, granted its stereo only.
Double check that your speaker/amp inputs match your sound card outputs to prevent similar problems.
Good Luck!