AMD's CPUs don't support more than 5600 MT/s without overclocking; they're still using the same IO die from Zen 4, so their memory controller is pretty outdated. Zen 6 should introduce a new IO die with a better memory controller, but for now 6000 MT/s is the fastest reasonable memory overclock for AMD desktops.

Intel's desktop CPUs from last year support up to 5600 MT/s with regular DDR5 DIMMs, or 6400 MT/s for CUDIMMs. Speeds higher than this are achievable, but are overclocking.

If your memory modules are rated for 6400 MT/s, they are most likely advertising the speed when using an Intel XMP or AMD EXPO profile to overclock the memory (and the CPU's memory controller). The JEDEC standard profile likely is no faster than 5600 MT/s. It's also possible that you bought last year a kit of CUDIMMs rated for 6400 MT/s without overclocking, brand new to the market at that time, and of no help whatsoever with any CPU that isn't an Intel Arrow Lake.

Though clarified at the start about Desktop, but missed JEDEC applying, of course, generally for the whole post.