a 5.1 computer speaker setup or 5.1 home audio speaker setup?
if a speaker setup such as the ones logitech makes you would need a 5.1 capable soundcard. they do make external usb powered soundcards you could use.
if a home theater setup you could use spdif output but it may be advisable to run the audio/video signal out of your graphics card via hdmi or dvi-to-hdmi cable to the receiver and then have a hdmi from the receiver to your monitor. this is the route i use personally
you can see my setup here
what do you mean by a single aux slot? a photo or better yet the model and brand of your pc or if self built the brand and model of your video card, soundcard and motherboard. in any case, no you can not power a 5.1 system from one 3.5mm port.
a soundcard is required if you use pc speakers but may be included onboard your motherboard. an add in pci soundcard has better sound capabilities but is not required. again, this is for pc speaker use. for home theater system use there are other options which are better suited.
a home theater systems receiver processes the sound which is why you dont need to export via the soundcard.
you want to list:
-your maximum budget
-physical space you have to work with
-what you want speakers for (games music etc)
-are you an audiophile?
-do you want to use pc speakers or home theater speakers?
-anything else you feel is relevant