This problem involves translating a word problem into algebra. Let's take it one statement at a time.

The first number, we learn at the end, is x. If x is one-third the value of the second number, then the second number is 3x.

If 3x is 5 less than the third number, then the third number is 5 greater than 3x, or 3x + 5. Finally, we are told that twice the third number, or 2(3x + 5), is equal to 5 less than 3x, or 3x - 5.

So, we can write the equation, 2(3x + 5) = 3x - 5.

Every answer choice, however, has 5 by itself on the right of the equal sign, so if we move terms around (i.e. add 5 - 2(3x + 5) to both sides), we have 3x - 2(3x + 5) = 5, answer choice (D).

The correct answer is (D).