The product mentioned, "HyperX Cloud II Core (Wired)," is not clearly identified in the sources provided, but we can deduce some information based on similar HyperX products.

The HyperX Cloud Stinger 2 Core and HyperX Cloud II Wireless headsets are compatible with the PS5, according to the official specifications.

If the "HyperX Cloud II Core (Wired)" is a variant of the HyperX headsets, it is likely that it is also compatible with the PS5, but without explicit confirmation in the sources, we recommend checking the product specifications directly on the manufacturer's website or in the product documentation.

In short, it's likely that the headset is compatible, but further verification is required for definitive confirmation.