Answer : The correct option is, the 5 kg object has more kinetic energy.
Explanation :
Formula used for kinetic energy is:

where,
K.E = kinetic energy
m = mass of an object
v = velocity of an object
Now we have to calculate the kinetic energy for 5 kg object with velocity 10 m/s.


Now we have to calculate the kinetic energy for 10 kg object with velocity 5 m/s.


From this we conclude that, 5 kg object with velocity 10 m/s has more kinetic energy as compared to 10 kg object with velocity 5 m/s.
Hence, the correct option is, the 5 kg object has more kinetic energy.