Will Displayport on a laptop output 5.1 surround sound?

[strike]Negative, displayport does not carry output sound, only HDMI is designed for both sound and video on the same connection.
Your only hope would be to use the headphone 3.5mm jack output to then your input on the home theater system and an DP>HDMI converting cable[/strike]

I was wrong, http/www.cnet.com/news/hdmi-vs-displayport-vs-dvi-vs-vga-which-connection-to-choose/ as it does carry sound. The only problem is no manufacturer normally makes a display INPUT port on a TV or Monitor like that, normally they are implementing either VGA, HDMI or DVI (monitors). As noted here by the DP Organization website: http/www.displayport.org/faq/
Q: I’d like to know if I use a DP –> HDMI adaptor to connect my computer to my TV, will I hear the sound with my TV or my computer?
A: DisplayPort does handle full HDMI signaling including sound but keep in mind that implementation of full HDMI signaling is an option the PC manufacturer must choose to enable. It is recommended that you check with the PC manufacturer prior to making a purchase and verify that the PC supports DP++ capability with HDMI. DisplayPort adaptors simply passes through the DVI or HDMI signal. We have published a DP Audio User Guide (http/www.displayport.org/wp-content/uploads/2011/10/DP-Audio-User-Guide-v1.pdf) for help on this topic.

TO me it seems DP just isn't the 'norm' anyone is really into and you will be hacking it to make it work (looking at emphes_is solution for example) and costly (Optical).

You can definitely get two channel sound with your 1080p signal, as that is exactly what I'm doing at the moment. I believe the spec is capable of six or eight channels, but running through my TV and out via optical is currently only giving me stereo.