Connection DVD ➡️ PC ➡️ TV

i am guessing that you want to get sound from your pc to play over your home theater? (otherwise you would just be connecting sony > tv)

the hdmi jack on the sony is for outputting video signal and is not for receiving an input from the pc. as far as i can tell it does not support hdmi (arc) either [audio return channel] which means you're completely SOL when it comes to 5.1 input. in short: cant be done unless it (and your tv) had arc support.

your dvd player does have stereo input which means you could play stereo sound from your pc over your home theater but i do not think this is what you were looking for.

unfortunately this problem plagues cheap HTIB [home theater in a box] systems and there are at least a few of these posts every week regarding connectivity. if you want 5.1 support over hdmi you would need to replace the receiver box/dvd player combo on that set with an AVR (and likely a separate dvd player). you can find cheap receivers like refurbished 523-k pioneers for $130-150 or get cheap knock off brands for a bit cheaper yet though i'd suggest staying with name brand.