I think you’re talking about telephone company switches. A “Class 5 Office” is a local telephone company switch which handles local station loops, etc. The “Class 4 Office” is the major long distance switch that processes calls to and from Class 5 offices, and would be a long distance company’s switch. This hierarchy of switches was, I believe, made up by AT&T prior to divestiture. It goes up to Class 1 which is a regional switching center.