Nikon 1 J3 has a 14.0MP 1" (13.2 x 8.8 mm ) sized CMOS sensor . On the other hand, Nikon 1 J5 has a 21.0MP 1" (13.2 x 8.8 mm ) sized BSI-CMOS sensor and features Expeed 5A processor.
Nikon 1 J5's sensor provides 7MP more than Nikon 1 J3'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.
One other difference between these two cameras that is worth mentioning is that Nikon 1 J5's sensor doesn't have an 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 1 J3 and J5 sensor size comparison.
Nikon 1 J3 and Nikon 1 J5 have sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture. On the other hand, since Nikon 1 J3 has 45% larger pixel area compared to Nikon 1 J5, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.
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. Nikon 1 J3 and Nikon 1 J5 sensors have been tested by DxO and the results show that J5 has a better overall score of 65, 13 points higher compared to 1 J3's score of 52.