Hello EthanBlomme,
Thanks for posting in the Apple Support Communities.
Have you tried using the camera of your device to set up the Apple Music app on your PlayStation 5? If not, give that a try and confirm you're using these steps: Get the Apple Music app on your smart TV, game console, or streaming device - Apple Support
Set up the Apple Music app
1. Go to your device's app store and download the Apple Music app. If you don't see the Apple Music app, then your device might not be supported or the Apple Music app isn't available in your country or region.
2. Open the Apple Music app.
3. Follow the onscreen steps to sign in with your Apple ID and complete setup:
• Sign in using your mobile device: Use the camera on your phone to scan the QR code on your screen. Then follow the instructions on your mobile device to sign in with your Apple ID and finish setup.
If that isn't helpful, try resetting the Apple Music app with the steps of the previous resource.
Have a great day!