If your HDMI cable from the GPU Card is connected directly to the TV, that is why it will show Stereo. It isn't seeing what is connected from the output from the TV to your PS4 or XBox.
In my case, I have one HDMI cable from my GPU card connected to my Onkyo A/V Receiver and made "default Audio Device" and then I have another HDMI cable from my second GPU card output HDMI to my TV. Thus I have both 5.1 sound while the TV and Monitor are on. But the TV & Monitor speakers don't work since I have the A/V Receiver as default.
Unfortunately, you can only have one "Default Audio Device". You may want to connect directly to the PS4 or Xbox, whichever has the 5.1 audio, directly from the GPU card and make it the "Default Audio Device". If the PS4 or Xbox has video output, then connect it to the TV.
In my case, I have from my GPU card:
1- HDMI cable connected directly to my Onkyo Receiver and made the "Default Audio Device"
2- HDMI cable connected directly to my TV
3- DisplayPort cable to my monitor.
Before I got my DP Monitor and had a previous HDMI Monitor, I had my HDMI cable connected directly from my GPU card to my Onkyo Receiver input (making it my default audio device in Sound panel). Then from my Onkyo Receiver HDMI Output I had an HDMI cable connected to my Monitor. Then I had a second HDMI cable connected from my GPU Card to my TV. The only sound I had was from my Onkyo Receiver while still getting Video to my monitor and/or TV.
You can use an Active adapter to convert one of the Non-HDMI video outputs on your GPU card to HDMI to connect your PS4 or XBox or TV.