FCP doesn't work well with the native files that camera shoots. Unfortunately is APPEARS like it will, but it won't. Yeah, it'll import fine, and you might begin editing fine, but things will pop up, like a sluggish system, loss of sync while editing, loss of sync when trying to export.
Do not cut the native H.264 MOV files the camera shoots with. FCP demands FCP editing codecs, and the one you want is ProRes 422. You'll need to use COMPRESSOR for this, as Log and Transfer doesn't support the 5D Mark III. Now, the bad news is that that 8GB of footage will become about 32-40GB...because the format you are converting to has a higher data rate. This is unavoidable, if you plan on using FCP 7. Premiere Pro will cut this format natively...and FCX can, but FCX does still want to "optimize" the media, and by that it means convert to ProREs.
Gotta convert to ProRes 422 before you import the footage.