The typical digital output you see is either a square Toslink connector, or a dual use 3.5mm TRS connector. The cable Dr. Strangelove links to an image of won’t work here however. What you need as a 3.5mm to square Toslink cable. The 3.5mm socket actually has an optical output LED in the back and the optical cable plug is a little longer than a normal 3.5mm TRS and goes right back to meet the LED. There are also adaptors that fit over the square end of a Toslink cable to convert it to a 3.5mm optical.
However you need to see if your PC does actually output optical like this. As noted above, it is pretty common.
Be aware that the Toslink digital link can only support a limited set of 5.1 sound encodings, and won’t support the high resolution (lossless) surround sound that HDMI can (such as True-HD). It will support the lossy compressed sound (up to Dolby Digital Plus), and that is usually fine for most people anyway.
OTOH, if you get at all stuck, you could probably look at even the cheapest of new sound cards to ensure you have what you need.