Both Nikon D5500 and Nikon D750 have 24.0 MP resolution sensors but Nikon D5500's sensor is APS-C (23.5 x 15.6 mm ) and Nikon D750's sensor is Full frame (35.9 x 24 mm ).
Since Nikon D750's has a larger sensor area with the same resolution, this means that it also has a larger pixel area hence better light collecting capacity for a given aperture compared to Nikon D5500.
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 D750 sensor size comparison.
As seen above, Nikon D750 has a 2.4x Larger sensor area than Nikon D5500. 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.