Canon 1D MIII has a 10.0MP APS-H (28.7 x 18.7 mm ) sized CMOS sensor . On the other hand, Nikon D5 has a 21.0MP Full frame (35.8 x 23.9 mm ) sized CMOS sensor and features Expeed 5 processor.
Nikon D5's sensor provides 11MP more than Canon 1D MIII's sensor, which gives a significant advantage in real life. You can print your images larger or crop more freely.
On the other hand, please keep in mind that Max sensor resolution is not the only determinant of resolving power. Factors such as the optical elements, low pass filter, pixel size and sensor technology also affects the final resolution of the captured image.
Below you can see the 1D MIII and D5 sensor size comparison.
As seen above, Nikon D5 has a 1.6x Larger sensor area than Canon 1D MIII. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.
DxOMark Sensor Scores
DxOMark is a benchmark that scientifically assesses image quality of camera sensors. It scores camera sensors for color depth (DXO Portrait), dynamic range (DXO Landscape) and low-light sensitivity (DXO Sports), and also gives them an overall score. Canon 1D MIII and Nikon D5 sensors have been tested by DxO and the results show that D5 has a better overall score of 88, 17 points higher compared to 1D MIII's score of 71.