Nikon D5200 has a 24.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor and features Expeed 3 processor. On the other hand, Nikon D5100 has a 16.0MP APS-C (23.6 x 15.7 mm ) sized CMOS sensor and features Expeed 2 processor. Nikon D5200's sensor provides 8MP more than Nikon D5100'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 D5200 and D5100 sensor size comparison.
Nikon D5200 and Nikon D5100 have almost the same sensor size so none of them has any significant advantage over other in providing control over depth of field when used with same focal length and aperture.