Running a 220v dust collector with 24v switches
I suggest you go to Lumberjocks (http://www.lumberjocks.com) where you will find many woodworkers with experience controlling dust collectors.  Search their forums for discussion on the topic, and the projects and blogs - I recall seeing descriptions of dust collection systems there...

For a 5 hp motor, you will certainly need a proper motor starter (contactor) which can be controlled by 24 V.  A 240/24 or 120/24 volt transformer would be used to power the control circuit.