The Raspberry Pi 5 can run PlayStation 2 games fairly well, although many games still have issues running smoothly. The Raspberry Pi 5 also does pretty well with the GameCube and Dreamcast. But, it turns out the original Xbox is a little more demanding.
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One resource for emulation is EmuGen Wiki, whose Xbox page says there’s only stable Xbox emulation via Xemu on x86/Intel/AMD systems. The Raspberry Pi 5 is powered by a chip called ARM64, and so are not able to emulate the Xbox well yet. If you look hard enough, you can find Reddit posts from developers attempting to port the Xemu source code to ARM64, but it’s very hard.
If you dig further, you can see that some YouTubers have gotten it running, but with some big caveats. One YouTuber, leepspvideo, was able to get Xbox games running, but they were too slow to play. The good news is that powerful ARM64 chips, such as those in Apple’s MacBook Air laptops, do a much better job. So, future Raspberry Pi boards will likely be more capable.
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A different YouTuber, Wooty B, got it running fairly well on ARM64 using a powerful, and expensive, HoneyComb workstation. But unless you’re willing to throw thousands of dollars at this DIY project, a standard Raspberry Pi is probably unlikely to reach that kind of performance anytime soon.