Nikon D5500 has a 24.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor and features Expeed 4 processor. On the other hand, Olympus E-M10 MIII has a 16.0MP Four Thirds (17.4 x 13 mm ) sized CMOS sensor and features TruePic VIII processor. Nikon D5500's sensor provides 8MP more than Olympus E-M10 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.
Another difference between these two cameras is that Nikon D5500's sensor lacks anti-alias (Low-Pass) filter. Removing anti-alias filter increases the sharpness and level of detail but at the same time, it increases the chance of moire occurring in certain scenes.
Below you can see the D5500 and E-M10 MIII sensor size comparison.
As seen above, Nikon D5500 has a 1.6x Larger sensor area than Olympus E-M10 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.