I have managed to (somehow) cross-compile Qt5 with the Mingw-w64 Project\'s compiler for 32-bit Windows. All of the libraries have been installed to ~/i686-w64-mingw32
In the end, it turned out that the problem was caused by a wayward libstdc++-6.dll somewhere in $PATH. After ensuring that the copy built by Mingw-w64 was in the application's directory, everything worked.