No, Qt5 is inside that install -- doesn't matter where you put it, it's still the same program executables, and if it was downloaded from calibre-ebook.com it uses its own Qt5.
If it is a distro install, it uses the system Qt5 -- or there is no distro calibre 2.
If it is crashing, the problem most likely has to do with your version of glibc -- that is the only thing the calibre binaries have a dependency on. (This is mentioned in the notes on the download page.)
Earlier versions of calibre could make do with earlier glibc versions.
Doesn't really matter what specifically made it fail though.
