Olympus TG-5 has a 12.0MP 1/2.3" (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features TruePic VIII processor. On the other hand, Fujifilm X-E2S has a 16.0MP APS-C (23.6 x 15.6 mm ) sized CMOS X-TRANS II sensor and features EXR Processor II processor.
Another difference between these two cameras is that Fujifilm X-E2S'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 TG-5 and X-E2S sensor size comparison.
As seen above, Fujifilm X-E2S has a 13.1x Larger sensor area than Olympus TG-5. 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.