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Does it make sense to upgrade my ethernet cables?
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If it's actually Cat.5 then it may be worthwhile to look at replacing with something newer, but if you're on Cat.5e then unless you wanna start playing with 10Gbit you'll probably be fine.
If you do upgrade, you don't need to go to Cat.8 simply because it exists. Cat.6a or even plain Cat.6 will do everything you're gonna need in Gbit networks.