Back when computers were slower, all of those calculations were too expensive to be conducted by the CPU. So you wanted a specialized ASIC to run the RAID5 checksum algorithms (aka: a RAID controller). But today, modern CPUs have so much spare compute power, you really don't want to be using a RAID controller anymore. In fact, many RAID systems on cheaper motherboards are just software RAID (a device driver that performs this RAID calculation, except it only works on a given motherboard that the device driver was made for). As such: RAID is just a bad idea: if the motherboard dies, there's no guarantee that a future motherboard knows how to read your RAID collection.
In contrast, a modern filesystem like ZFS (Linux/BSD) or ReFS (Windows enterprise storage spaces: "REsillient File System"), will be able to be rebuilt on a new motherboard automatically. If your "RAID" is all software anyway, might as well embrace the software-based methodology to the logical extreme and just use these features afforded by the operating system.
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So when people today talk about "RAID5", they really mean running ZFS in 1-disk parity mode or Storage Spaces in 1-disk parity mode. I don't think people really mean buying a hardware RAID system anymore (ex: LSI MegaRAID or whatever). These software only solutions have been getting better and better (moreso on Linux, but ReFS / Windows Storage Spaces still has nice features worth talking about).
I recommend building a system with ZFS: be it Linux ZFS or BSD ZFS (Xigmanas is what I use) and really playing around with it. I also recommend 4-hard drives in striped+mirrored (aka: RAID10-like setup), which will only fail if 2x hard drives fail. striped+mirrored works efficiently in all software systems (Windows Storage Spaces and Linux), so its a good default. Linux's RAID5-like and RAID6-like software setups are known to be pretty efficient (Windows Storage Spaces not so much so). If you're going beyond 4-hard drives, working with Linux for 2x parity drives on say a 8-HDD setup is likely going to be less of a headache than 2x parity drives on Windows Storage Spaces. Windows works, but something about its algorithm is a good bit slower IIRC in this case.
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The main advantage of ZFS or ReFS is that Linux/Windows/BSD is more aware of the disks. In particular, the "ZFS Scrub" command will automatically scan all data and check for bitrot (and automatically correct any issues that come up). If you were using a hardware RAID system like LSI MegaRAID, Linux wouldn't necessarily know how to scrub / rebuild (it'd be part of the controller). There are also advanced software features like ZFS snapshots available.