For the PSU question, this calculator says you are safe on power consumption Newegg PSU calculator
I think your upgrade makes sense, just some notes:
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If you are comfortable, check the second-hand market. CPU, boards and RAM sticks barely degrade over time, just make sure to personally test the hardware.
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The 5600 comes with a stock cooler. No need for a new one, unless you want less noise and lower temps.
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The 5600x is not worth it, save the $10.
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If possible, look the 5700x. It's almost the same CPU, but with 2 extra cores. Also includes stock cooler.
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Note that the AM4 platform won't get new CPU launches. That means that, if in a future you want to upgrade you CPU again, you'll have to buy a new board, again. The AM5 platform is brand new, so you'll be able to get a better CPU in a future without having to buy a new board. This comes with two caveats:
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AM5 boards and CPUs are more expensive, plus your current RAM won't work, as AM5 does not support DDR4 sticks.
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You would be buying in AMD's promise to launch new CPUs in AM5. While AMD has a good records keeping these promises (and I would personally trust them here), keep in mind they are a mega corporation after all.
I have no idea about the PSU cables.
Hope this helps :)