Solution:

We need to find the remainder when 38n^3 - 2 is divided by 5.

Let's first simplify the expression 38n^3 - 2.

38n^3 - 2 = (40n^3 - 2n^3) - 2
= 2n^3(20 - 1) - 2
= 2n^3(19) - 2

Now, we need to find the remainder when 2n^3(19) - 2 is divided by 5.

Let's consider the remainders of 2n^3 and 19 when divided by 5.

When 2n^3 is divided by 5, the remainder can only be 0, 2, or 3.

When 19 is divided by 5, the remainder is 4.

Using these remainders, we can find the remainder when 2n^3(19) - 2 is divided by 5.

Case 1: When 2n^3 leaves a remainder of 0 when divided by 5

In this case, 2n^3(19) - 2 leaves a remainder of (-2) or 3 when divided by 5.

Case 2: When 2n^3 leaves a remainder of 2 when divided by 5

In this case, 2n^3(19) - 2 leaves a remainder of (2x4 - 2) or 6 when divided by 5.
But 6 leaves a remainder of 1 when divided by 5.

Case 3: When 2n^3 leaves a remainder of 3 when divided by 5

In this case, 2n^3(19) - 2 leaves a remainder of (3x4 - 2) or 10 when divided by 5.
But 10 leaves a remainder of 0 when divided by 5.

Therefore, the possible remainders when 2n^3(19) - 2 is divided by 5 are 0, 1, or 3.

But we know that the correct answer is option 'D' or 4.

So, the only possible remainder left is 4.

Hence, the remainder when 38n^3 - 2 is divided by 5 is 4.