If rpm required is 25 at the output of gear box attached to a 5HP motor, Which of the following motors suit the best considering amount of power (electricity/ energy saving):

A) 5HP 2POLE MOTOR
B) 5HP 4POLE MOTOR
C) 5HP 6POLE MOTOR
D) 5HP 8POLE MOTOR

Kindly please answer along with justification/ proof.

Thank you

Aman, the real question is how much torque is needed to do the job. But sticking to your question, the 4-pole 5 HP motor will have the highest efficiency band of the 2-, 4-, 6- or 8-pole options.
I would avoid using the 2-pole in part because of the likelihood of reduced bearing life or higher maintenance requirements. And the 6- or 8-pole motors are more expensive, require a larger frame than the 4 pole, and will have lower efficiency.
Chuck