The built-in wi-fi on XBOX360 models that have that feature does uses only the 2.4ghz spectrum. I have read reports that the black XBOX 360 N adaptor does support 5ghz but I find that quite dubious since mine clearly does not and I found no product literature that says otherwise when I searched.
How to connect your Xbox to a hotel wireless network Choose a phone or other device to mimic, then find its MAC address. On a Windows phone, you can … How to Hook Up a Wireless Xbox 360 Controller to Your Computer Jul 10, 2017 How to Connect an Xbox 360 to Your TV - lifewire.com Mar 27, 2020 Xbox 360 can't connect to WiFi - Solved - Fizz Community Hub
How to Set up Xbox Live using a laptop and ethernet cable
How to Connect Xbox 360 to Internet Without Wireless Method 1 Plug the LAN or ethernet cable to the laptop or desktop computer and the Xbox 360. Turn on the laptop or desktop computer and the Xbox 360. As soon as you’ve logged in to Windows, click the Windows Start button located at the bottom-left corner of the screen Type control panel and hit How to Connect an Xbox 360 to an XFINITY WiFi Hotspot: 6 Steps Dec 08, 2015