I don't know the installed packages on your system but what I can help only - Download Qt 5.5 installers from "https://download.qt.io/archive/qt/" and install it on custom path ( e.g. /opt/Qt5.5" and use "qmake" installed in that directory during compilation and let us know result.
OK, different errors now, but still the qt warning
(pgadmin4) wbloos@wb:~/python-files/pgadmin4/runtime$ /opt/Qt5.5.1/5.5/gcc_64/bin/qmake "DEFINES +=PGADMIN4_USE_WEBKIT" Project MESSAGE: Building for QT5+... Project MESSAGE: Forcing use of QWebKit... Project MESSAGE: Project MESSAGE: ************************************** WARNING ************************************** Project MESSAGE: * It is strongly advised that Qt 5.5.0 or later is used to build the pgAdmin runtime. Project MESSAGE: ************************************************************************************* Project MESSAGE: Project MESSAGE: Building for Linux/Mac... Project MESSAGE: Using /home/wbloos/.virtualenvs/pgadmin4/bin/python-config Project MESSAGE: Python3 detected. (pgadmin4) wbloos@wb:~/python-files/pgadmin4/runtime$ make > make.log 2>&1