The rational number should be between 5 and 514, so it should be greater than 5 but less than 514.
Option a. 517 is greater than 514, so it is not a valid answer.
Option b. 525 is greater than 514, so it is not a valid answer.
Option c. 513 is less than 514, but 513 + (1/3) = 513.33 repeating, which is greater than 514. So it is not a valid answer.
Option d. √26 is approximately 5.099, which is less than 514. So it is a valid answer.
Therefore, the correct answer is d. √26. ,