Thanks Ian and Steve.
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My Linux distribution and package manager contains the old version. I did try compiling it from source and ended up in "dependency hell". I suspect any native package installer would be the same. :(
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The FlatPak idea sounded like an easy way around the dependency problem (that's part of its purpose, after all), but I don't want a SaaS model (Software as a Service). I like to have a download that I can archive to recreate the exact same system at any point in the future. That way I have an EXACT copy of what was installed and can always reproduce it (bugs and all).
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What surprised me (not knowing much about FlatPaks) was that they don't seem to be available as a straight download. KiCad is offered as a FlatPak on "flathub", so someone went through the trouble to build it (along with a Windows .EXE and others). But while the Windows EXE can be downloaded (and archived), the FlatPak itself is surprisingly elusive. I'm just not sure why (yet).
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Either way, my immediate problem is solved (Windows for KiCad 8, Linux for KiCad 5). So thanks for all the help!!