Check the actual new prices before assuming the older AM4 chip is the cheaper, safer choice, because right now it isn't. The 5600X runs $32.50 more new than the 7600X on ChipFlip's own tracked listings, meaning the "budget" platform currently costs more than the newer one.
The real numbers, not the assumption
That price flip alone should settle this for anyone buying new hardware today. On top of the price, ElectronicsHub's comparison found the 7600X ahead in both gaming and single-core performance, reaching notably higher clock speeds under load. The 5600X isn't a bad chip. It's a mature, well-supported AM4 part. It's just no longer the automatic value pick that platform age usually implies.
The one real catch: the platform, not the chip
AM5 needs a new motherboard, where AM4 has years of existing boards already in circulation. If a used AM4 motherboard is already in hand, or already owned, the 5600X's used price (a legitimately cheap $55.99 on ChipFlip's tracked listings) is still a strong budget play built around hardware you don't have to also buy.
Where AM5 pulls ahead long-term
AM4 launched in 2016 and is functionally done getting new CPU releases. AM5 is expected to keep receiving new chips through 2028 and beyond. Building fresh, with no existing AM4 board to reuse, means AM5 buys real future upgrade room the older platform simply can't offer anymore.
The takeaway
Buying new with no existing motherboard: get the 7600X, it's both cheaper and faster right now. Already sitting on an AM4 board: the 5600X used, at $55.99, remains one of the best cheap upgrades available for that exact platform.