I probably should have remember to add that I do have an adapter from 3x 3,5mm to RCA and a RCA to single 3,5mm cable (and yes, there is a headphone jack on the tv) so I can use the speakers. However, since a headphone jack only outputs 2 channel audio I can't get 5.1 output this way and I would like to be able to use the speakers to their full potential.
Two of the hdmi ports on the TV have ARC (I did not include it the first time as I did not know what that implied) if that makes a difference.
The only way I have been able to sort of solve this is to connect the speakers to a PC and plug that to the TV with hdmi. But then the speakers will only work for audio from the computer but not for the regular TV-broadcasts. That's why I want to connect the speakers directly to the TV.
As I wrote in the original post I do have an old PC that I could use for parts if that is possible. Even if I will have to solder something together I am willing to do that.