To solve this problem, you need to work backwards. One half of 1500 is 750. Two thirds of 750 is 500. One tenth of 500 is 50, and one fifth of 50 is 10. Finally, half of 10 is 5 making this the correct answer.
To double check, do the opposite of the operations. 5 times 2 is 10; 10 times 5 is 50; 50 times 10 is 500; 500 divided by two thirds is 750; and 750 times 2 is 1500.