Does the motor have a over temp pop out button on the end opposite the pulley?
Some good pics will help.
Being a two stage, the motor probably is a true 5 hp and may very well need a starter. The reason for one is two fold, first, the pressure switch would have to be huge to carry the amperage of the motor, so instead, a small, low amp rated pressure switch pressure is used and it operates the coil of the motor starter (simply a solenoid operated multiple contact switch) and the second need for a starter is that is contains a thermal overload, in the form of a heat element that is sized to the motor, so that if the motor is overloaded (such as the pressure switch sticking and the pressure going way too high) the heat element would get hotter than normal and cause a set of contacts to open, killing the circuit to the motor and stopping it. It simulates the motor overheating.
Charles
