Nikon S5200 has a
16.0MP 1/2.3-inch (6.16 x 4.62 mm ) sized BSI-CMOS sensor . On the other hand, Ricoh GXR P10 28-300mm has a
10.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features Smooth Imaging Engine IV processor.
Nikon S5200's sensor provides 6MP more than Ricoh GXR P10 28-300mm'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 S5200 and GXR P10 28-300mm F3.5-5.6 VC sensor size comparison.
Nikon S5200 and Ricoh GXR P10 28-300mm have almost the same sensor size, so neither of them has any significant advantage over the other in terms of providing control over depth of field when used with the same focal length and aperture.