To find the remainder when 712x^3 - 3 is divided by 5, we need to simplify the expression and then find the remainder.

Simplifying the expression:
712x^3 - 3 can be rewritten as (710x^3 + 2x^3) - 3.

We know that when a number is divided by 5, the remainder can only be between 0 and 4.

To find the remainder of 710x^3 when divided by 5, we can use the concept of modular arithmetic. In modular arithmetic, we take the remainder when a number is divided by another number.

Dividing 710 by 5 gives a remainder of 0. Therefore, the remainder of 710x^3 when divided by 5 is also 0.

To find the remainder of 2x^3 when divided by 5, we can divide each term of 2x^3 by 5 and take the remainder.

2x^3 = (2/5)x^3 * 5 + (2 mod 5)x^3

Since 2 divided by 5 gives a remainder of 2, we can rewrite the expression as:

2x^3 = (2/5)x^3 * 5 + 2x^3

Therefore, the remainder of 2x^3 when divided by 5 is 2x^3.

Now, let's combine the remainders:

(710x^3 + 2x^3) - 3 = (0 + 2x^3) - 3 = 2x^3 - 3.

To find the remainder of 2x^3 - 3 when divided by 5, we can use the same approach as before.

Dividing 2x^3 by 5 gives a remainder of 2x^3.

Dividing -3 by 5 gives a remainder of -3.

Since the remainder has to be between 0 and 4, we can add 5 to the remainder -3 to get a positive remainder:

-3 + 5 = 2.

Therefore, the remainder when 712x^3 - 3 is divided by 5 is 2.

Hence, the correct answer is option B) 2.