If you're watching a movie, configure the movie playback software to use the HD audio device built into your graphics card, then use the HDMI port to connect with your amplifier, and finally from your amplifier to your display device. It will carry the encoded audio of a movie to your amplifier without a bunch of fuss.
Your other option is to run digital audio from your sound card to your amp, but it doesn't look like your audio on the computer has a digital output on it. If that's the case, that option is out unless you wish to purchase an add-in board audio card that has digital audio out. Once you're running digital audio to your amp from a sound card, you will still have to encode your computer's audio to receive 5.1 on your amplifier, using either Dolby Digital Live or DTS Connect, depending on the format supported by your amplifier. DDL or DTS Connect is a feature you will have to look for on any sound card you wish to purchase, if you need that feature. It's not necessary when watching a movie, as movies are pre-encoded on the disc, but if you wish to play computer games or music with surround sound, you will need to encode them in real-time as the audio is sent to the amplifier.