Don't buy DDR5 for gaming. The performance uplift is there, but it doesn't warrant an upgrade. Yes, DDR5 helps improve your frame rates, but you also need to keep your expectations in check. So unless you're a hardcore gamer that doesn't like knowing you're leaving performance on the table, you shouldn't pick up DDR5.
This is something you can easily mitigate when you buy DDR5 that is faster than 4800 MHz, e.g 5600/6000 Mhz and enable the faster RAM profile from BIOS, so that the RAM actually runs at advertised speeds.
For now, DDR4 offers more bang for your buck. For comparison, the cheapest DDR5-4800 32GB C40 memory kit retails for $73, whereas a DDR4-3200 32GB C16 memory kit goes for as low as $50. While the former offers 6% higher performance, it's also 46% more expensive than the latter. DDR5 pricing won't remain this high forever, but DDR5 can't compete with the value of high-end DDR4 until it improves.
This quote is somewhat true. Then again DDR3 is even cheaper than DDR4, but it doesn't mean one should go with DDR3 MoBo (latest MoBos that support DDR3 would be Intel 100-series chipset, supporting Intel 6th gen Skylake CPUs).
E.g the DDR5 i put into my 2nd suggestion, it costs €117. That's €18 more than the DDR4 kit you picked initially. Of course, frequency is far higher for DDR5, at 6000 Mhz, compared to 3600 Mhz DDR4 you picked. So, as of current date, DDR5 prices have come down quite a lot, making DDR5 worthwhile (price wise).
DDR5 has more future-proofing value. However, manufacturers haven't rung DDR4's death knell. It's undeniable that the next generations of processors will eventually drop DDR4 support. Upgrading to a DDR5 memory kit today means you can reuse it for future platforms. The downside is that DDR5 is still wet behind the ears, so there will be better offerings down the line.
This is true. DDR5 launched a while back and if you go with AMD, you don't have an option between DDR4 or DDR5.
AMD Ryzen 1000, 2000, 3000 and 5000-series CPUs support only DDR4. (Using old AM4 socket.)
AMD Ryzen 7000-series CPUs support only DDR5. (Using new AM5 socket.)
With Intel, you have an option;
Intel 12th gen, 13th gen and 14th gen work on Intel 600- and 700-series chipset MoBos. Both chipset series MoBos offer DDR4 and DDR5 MoBos. (Using LGA1700 socket.)
So, future proofing wise, if you go with Ryzen 5000-series CPU (like 5800X3D you picked), you're stuck with dead platform. Ryzen 7000-series CPUs work only with AM5 socket MoBos, while your MoBo would be AM4 socket.
With Intel, latest CPU generation is 14th series and 600- and 700-chipset MoBos work with it. Perhaps even upcoming 800-series chipset as well. But when Intel moves on to 15th gen CPUs and 900-series chipset MoBos, Intel usually changes CPU socket and you can't upgrade your CPU, without replacing MoBo as well.
With this, and IF you plan to upgrade CPU at later date, your best bet would be going with Ryzen 7000-series and AM5 MoBo (which only supports DDR5). Since with that, you can be sure that the next CPU generation (perhaps even 2 or 3 next generations) are supported by your MoBo.
Though, most people doesn't upgrade their CPU that easily, instead like to keep the CPU running for 5-10 years. By that time, far different CPUs/MoBos/RAM are available (e.g DDR6) and it would be easier to go with new CPU-MoBo-RAM combo.