From the look of things you can, I know Abelcine posted a photo of that setup. Not sure about balancing though.
According to specs on BH the C300 is larger: C100: http://www.bhphotovideo.com/c/product/889545-REG/Canon_EOS_C100_EF_Cinema.html C300: http://www.bhphotovideo.com/c/product/839220-REG/Canon_5779B002_C300_Cinema_EOS_Camcorder.html
I bet it will fit. I haven't seen the motors on the m10 vs m5 but I'm assuming they are the same. Maybe the power is restricted in the software….but larger cameras are definitely not going to fit in the smaller frame.
Chris, approximately 125mm from the base plate to the bottom of the top plate. Sam you would lose the increased rigidity. The Canon C series from their specs is to tall. It is not on the compatibility chart for the M5. It is on the chart for the M10.