Good purchase. Hopefully you have learned more about this camera in the last month.
Using a solid tripod will also help when doing long exposures. Both mirror lockup and time delays are available through the menu.
Mirror lockup will require 2 shutter presses. 1st one raises the mirror and 2nd one opens the curtains for exposure.
I use a remote switch so I don't touch the camera but the time delay works too.
Using a long lens also makes it more difficult to keep any shake out.
Here is a 25 second exposure at ISO 100 where I used a gimbal head on a carbon fiber Manfrotto tripod and Canon 300mm F/4 L lens. I used mirror lockup.
The 5D Mk III is awesome.