The error is telling you that the runtime environment of your process cannot find the platform plugin. The platform plugin and source file is part of Qt5.
If you are running the program in your IDE then you have a broken installation.
If you are running the program in a deployed environment then you have failed to deploy the necessary plugin(s).


The relative MOC_DIR path is not inherently wrong. That path is relative to the current working directory in which qmake is run. If your IDE is running qmake with the current working directory set to somewhere that cannot be written then there is a misconfiguration of either the IDE or the project settings (e.g. a broken shadow build path).