The Logitech X530 uses analog 3.5 mm inputs, while Xbox consoles output digital audio via optical (TOSLINK). You cannot connect them directly.
Notes: The X530 cannot decode Dolby/DTS; PCM stereo/5.1 works. Audio quality may be slightly lower than a dedicated AV receiver. Ensure speaker configuration in Windows is set to 5.1 Surround for PC use.