/usr/lib/gcc-cross/ is in libobjc-5-dev-s390x-cross 5.5.0-12ubuntu1cross1.
This file is owned by root:root, with mode 0o755.
..
/usr/lib/gcc-cross/s390x-linux-gnu/
/usr/lib/gcc-cross/s390x-linux-gnu/5/
/usr/lib/gcc-cross/s390x-linux-gnu/5/include/
/usr/lib/gcc-cross/s390x-linux-gnu/5/include/objc/
/usr/lib/gcc-cross/s390x-linux-gnu/5/include/objc/NXConstStr.h
/usr/lib/gcc-cross/s390x-linux-gnu/5/include/objc/Object.h
/usr/lib/gcc-cross/s390x-linux-gnu/5/include/objc/Protocol.h
/usr/lib/gcc-cross/s390x-linux-gnu/5/include/objc/message.h
/usr/lib/gcc-cross/s390x-linux-gnu/5/include/objc/objc-decls.h
/usr/lib/gcc-cross/s390x-linux-gnu/5/include/objc/objc-exception.h
/usr/lib/gcc-cross/s390x-linux-gnu/5/include/objc/objc-sync.h
/usr/lib/gcc-cross/s390x-linux-gnu/5/include/objc/objc.h
/usr/lib/gcc-cross/s390x-linux-gnu/5/include/objc/runtime.h
/usr/lib/gcc-cross/s390x-linux-gnu/5/include/objc/thr.h
/usr/lib/gcc-cross/s390x-linux-gnu/5/libobjc.a
/usr/lib/gcc-cross/s390x-linux-gnu/5/libobjc.so