Actually if you came from a considerably lower resolution camera, it might just be that the 5D needs more sharpening comparatively... You also might be looking at the images a lot larger than you were lower resolution images... so are effectively being more critical of them.
After all, you say that images sharpen up just fine.
However, if you are comparing 5DC to 50D, then neither of the above should apply. The 5DC RAW files should be as sharp or perhaps slightly sharper right from the camera.
But, yes, it's possible the camera and/or lens need calibration. Most cameras and lenses benefit from a tune up occasionally.
And, yes, a filter could be a problem.
Also, depending upon your typical uses... 5DC and 5D MkII have a big mirror so there is more mirror slap with them than with your APS-C camera. At some shutter speeds, most likely the 2 second to 1/30 range, it's possible you are seeing some small amount of shake blur from mirror slap. Mirror lockup and/or I.S. are the only ways to address that. The mirror light seal/dampener foam on cameras wear out over time, too, and need to be replaced. It's not a big job, so shouldn't be expensive.