Nikon 1 J5 has a 21.0MP 1' (13.2 x 8.8 mm ) sized BSI-CMOS sensor and features Expeed 5A processor. On the other hand, Samsung NX mini has a 20.5MP 1' (13.2 x 8.8 mm ) sized BSI-CMOS sensor .
Another difference between these two cameras is that Nikon 1 J5'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 moiré occurring in certain scenes.
Below you can see the J5 and NX mini sensor size comparison.
Sensor Size and Resolution Comparison image of Nikon 1 J5 and Samsung NX mini Cameras
Nikon 1 J5 and Samsung NX mini have the same sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture.