Every Intel Mac Mini has a combined digital/analog audio port and does indeed support optical output.
But, that doesn't help you. DVI does not output audio and I have not seen a DVI+optical audio to HDMI converter - primarily because it's pretty pointless sending a 5.1 audio signal to built-in TV speakers.
If your TV does not offer a separate audio input that works with at least one of your HDMI ports...
To get sound on the TV, you will need:
A converter similar to
this one. (All such converters require a power cable.)
Connect DVI-I cable from mini to the converter - if what you already have is a DVD-D cable, I think that will work also.
Need a 3mm stereo mini-plug to RCA audio cable to the box...
And your HDMI cable.