The XCB plugin fails on Qt 5.5 with an example that works on Qt 5.4.1:

$ /usr/lib/x86_64-linux-gnu/qt5/examples/gui/rasterwindow/rasterwindow
The X11 connection broke: Unsupported extension used (code 2)
XIO: fatal IO error 22 (Invalid argument) on X server ":0"
after 6 requests (6 known processed) with 0 events remaining.

I can also reproduce this failure with the minimal QtGui program:

#include <QGuiApplication>
int main() { QGuiApplication(); return EXIT_SUCCESS; }

Luckily, I was in a position to experiment with finding which unsupported extension it was trying to use, and, by a process of trial and error, found that adding enabling RANDR allows the program to run successfully.

If it is really, really necessary to depend on RANDR, please check for its presence and give an informative qFatal() if it's not there. Preferably, continue to work whether it's present or not, as Qt 5.4 does.