Yeah, this is quite a basic question, I know, but I haven't been able to find any information, not even in the BOINC forums.

Can I update the client without uninstalling the old version and reinstall the new one?

Yes. Although if you are going from a 5.nn BOINC to a 6.nn you will need to reboot the machine, for reasons which are totally bogus... but that is another story.

The upgrade process will move whatever files around as necessary. I have upgraded many many times, (including 5->6), and have never un-installed or had a problem. The "to be safe" crowd would probably advise you to make a copy of your BOINC directory and be prepared to move stuff around yourself if necessary. Hey, why not, costs little.

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Wave upon wave of demented avengers march cheerfully out of obscurity into the dream.