Both Sony A37 and Sony NEX-5R have APS-C sized 16.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
Below you can see the A37 and NEX-5R sensor size comparison.
Sensor Size and Resolution Comparison image of Sony A37 and Sony NEX-5R Cameras
Sony A37 and Sony NEX-5R have almost the same sensor size, so neither of them has any significant advantage over the other in terms of providing control over depth of field when used with the same focal length and aperture.
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. Sony A37 and Sony NEX-5R sensors have been tested by DxO and the results show that NEX-5R has a better overall score of 78, 3 points higher compared to A37's score of 75.
Model
Overall
Color Depth
Dynamic Range
Low-light ISO
Sony A37
75
23.3 bits
12.9 Evs
799 ISO
Sony NEX-5R
78
23.7 bits
13.1 Evs
910 ISO
Sensor size sets the circle of confusion, so it drives how much depth of field each
of these bodies gives you at a given aperture. You can calculate it exactly for the
Sony A37
or the
Sony NEX-5R ,
including hyperfocal distance.