Canon G5 X has a 20.0MP 1 (13.2 x 8.8 mm ) sized BSI-CMOS sensor and features DIGIC 6 processor. On the other hand, Canon G1 X III has a 24.0MP APS-C (22.3 x 14.9 mm ) sized CMOS sensor and features DIGIC 7 processor.
Below you can see the G5 X and G1 X III sensor size comparison.
As seen above, Canon G1 X III has a 2.9x Larger sensor area than Canon G5 X. 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.