Does shutting down and repowering CPU consume more energy?
My questions is, will leaving an idle computer with monitor shutoff
  due to 5 minute idle left for 30 minutes or so be more wise than
  shutting a computer down and turning it on after 30 minutes.


Even though most computers will throttle down the processor clocking and suspend a lot of other power using peripherals, you will still use less power having the unit off for the 30 mins or so. 

However constantly turning the computer on and off, may cause a bit more wear and tear on the unit, causing a reduced lifespan.