Two ways of doing what you want.
1) 3.5mm to RCA to a multi-channel amp or whatever amp config you need. Hook up the speakers, done. You could always go with studio monitors and avoid the amp, but that's a big purchase. The .1 channel can go directly to the sub and let the PC do all the bass management. I did this for a few years with a full 7.1 setup.
2) HDMI to an AVR and bypass the current soundcard. I've been doing this even long and have been much happier. AVR is MUCH better than my PC for bass management and room correction. The reason is because I'm either in my theater or office and the setup is less gaming and more toward watching TV/Movies.
I do have consoles in my office, but my PC is a stereo setup
because of how things are set up, I can't do surround for PC. BUT I can play on my TV and have full surround again. TV isn't as good as my monitor so there are trade offs.
For you, your PC is your main source and you're using a monitor. I'd go with #1 (even though, IMHO, it isn't as good) since you're controlling the volume with your keyboard. Just like I do when playing games. This will work quite well, but not as well as if you had a higher end DAC that had multichannel out support like a professional audio interface and studio monitors (just to simplify things). That lets you eliminate the AVR and amps all together. I've got friends that do that and love it.