This piece of output looks suspicious:
CFG_ARCH="i386"
Determining architecture... ()
g++ -c -pipe -g -Wall -W -fPIE  -I/builddir/build/BUILD/qtbase-opensource-src-5.0.0/mkspecs/linux-g++ -I/builddir/build/BUILD/qtbase-opensource-src-5.0.0/config.tests/arch -I. -o arch.o /builddir/build/BUILD/qtbase-opensource-src-5.0.0/config.tests/arch/arch.cpp
g++  -o arch arch.o    
{ test -n "" && DESTDIR="" || DESTDIR=.; } && test $(gdb --version | sed -e 's,[^0-9]\+\([0-9]\)\.\([0-9]\).*,\1\2,;q') -gt 72 && gdb --nx --batch --quiet -ex 'set confirm off' -ex "save gdb-index $DESTDIR" -ex quit 'arch' && test -f arch.gdb-index && objcopy --add-section '.gdb_index=arch.gdb-index' --set-section-flags '.gdb_index=readonly' 'arch' 'arch' && rm -f arch.gdb-index || true
    Found architecture in binary
CFG_HOST_ARCH="unknown"

Now investigating why the configure script can't determine the host architecture for s390x..

Do you happen to have shell access to a s390x environment which I could temporary use for debugging?

(In reply to comment #2)
> Do you happen to have shell access to a s390x environment which I could
> temporary use for debugging?

all machines I have are internal in RH, but the PPC people have public machines available, please ping them on #fedora-ppc on FreeNode

I'm not sure if the problem also exists on PPC..but then perhaps you could help me with the debugging.

Could you try to build the package locally (using fedpkg local/rpmbuild) and once it fails, please perform the following commands:

$ cd build_release_static_win32
$ g++ -pipe -g -Wall -W -fPIE  -I../qtbase-opensource-src-5.0.0/mkspecs/linux-g++ -I../qtbase-opensource-src-5.0.0/config.tests/arch -I. -o arch.o ../qtbase-opensource-src-5.0.0/config.tests/arch/arch.cpp -o arch
$ strings ./arch

The Qt5 configure script tries to locate the following text in the output of the 'strings' command:
==Qt=magic=Qt== Architecture
==Qt=magic=Qt== Sub-architecture

During the mock build which you tried earlier these two texts couldn't be located in the output of the 'strings' command.

What output does the 'strings' command give you?

Were you already able to do the test I described in comment 4 ?
Right now I'm prepping an update to Qt 5.0.1 and I would like to fix this bug at the same time as well

got distracted by other work, but it's on my list, will try to check it later today

I think I've found the root cause of this issue, but I'm not sure how to fix it. I just filed at bug upstream: https://bugreports.qt-project.org/browse/QTBUG-29426

Thanks, that corresponds to my understanding what was happening during the non-x86 builds.

mingw-qt5-qtbase-5.0.1-2.fc18 has been submitted as an update for Fedora 18.
https://admin.fedoraproject.org/updates/mingw-qt5-qtbase-5.0.1-2.fc18

Package mingw-qt5-qtbase-5.0.1-2.fc18:
* should fix your issue,
* was pushed to the Fedora 18 testing repository,
* should be available at your local mirror within two days.
Update it with:
# su -c 'yum update --enablerepo=updates-testing mingw-qt5-qtbase-5.0.1-2.fc18'
as soon as you are able to.
Please go to the following url:
https://admin.fedoraproject.org/updates/FEDORA-2013-2146/mingw-qt5-qtbase-5.0.1-2.fc18
then log in and leave karma (feedback).

I just pushed an updated package to rawhide and f18 which contains a fix which should allow cross-compilation on non-x86 hosts. I did a scratch build of it for the ppc target and it built fine without issues

for the record - build on s390/s390x was also successful

mingw-qt5-qtbase-5.0.1-2.fc18 has been pushed to the Fedora 18 stable repository.  If problems still persist, please make note of it in this bug report.