I chose to buy the pulse over the adapter. Even though its higher priced.
I got this one for PS4, it was pretty good.
Amazon.com: (Renewed) astro Gaming A50 Wireless Dolby Gaming Headset - Black/Blue - PlayStation 4 + PlayStation 5 + PC (Gen 3): Electronics
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I bought them (Previous model 300$) 5 years ago for my PS4. Ultimately werent very impressive. I think they are better for music than gaming on console. Probably needs a amp. Or the fact Audio was coming from the controller plug didnt help.
Buy Philips X2/27 Fidelio Headphones, Black: Over-Ear Headphones - Amazon.com ✓ FREE DELIVERY possible on eligible purchases
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Think its between these headsets for PS5.
Amazon.com: SteelSeries Arctis Pro + GameDAC Wired Gaming Headset - Certified Hi-Res Audio - Dedicated DAC and Amp - for PS5/PS4 and PC - Black: Video Games
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Amazon.com: SteelSeries Arctis 7P Wireless - Lossless 2.4 GHz Wireless Gaming Headset - for PlayStation 5 and PlayStation 4 - White - PlayStation 5: Video Games
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Amazon.com: Sony PULSE 3D Wireless Headset: Video Games
www.amazon.com
I settled on the Pulse since it has 3d audio.