Good day !
You say you have edited them, have you cropped them ?
I've printed 11x14 of images that I've cropped 1/4 of from images taken with my 40D (10MB) and they look fine.
You say large to enormous, how many inches by inches is large and how many inches by inches is enormous ?
The 5D MKIII is a 22MB sensor, creating images that are 5760 pixels x 3840 pixels, you could print 19 inches wide by 13 inches at 300dpi with NO problem at all, very crisp, if you don't crop. Now, you can also print bigger than that without noticing any artifacts.
Often, when printing something like a poster size, you can go to 200dpi and at a reasonable viewing distance, the image is crisp.
There's plenty of resources about printing digital images and the amount of pixels required to print a specific size, or even formulas that will help you figure out.
A good page with info that I found, and is 6 years old but still relevant, is http://www.bythom.com/printsizes.htm