Both Nikon D5500 and Nikon D5300 have APS-C sized 24.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
Another similarity between these two cameras is that both Nikon D5300 and Nikon D5500 sensors lack anti-alias (Low-Pass) filters. 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 D5300 sensor size comparison.
Nikon D5500 and Nikon D5300 have sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture.