The difference between LCM and HCF of 48 and 60 is:

$$5 - 2(3x - 1) = -13$$ $$5 - (2 \times 3x) - (2 \times -1) = -13$$ $$5 - 6x + 2 = -13$$

$$(5 + 2) - 6x = -13$$ $$7 - 6x = -13$$

$$7 - 6x - 7 = -13 - 7$$ $$-6x = -20$$

$$\frac{-6x}{-6} = \frac{-20}{-6}$$ $$x = \frac{20}{6}$$ $$x = \frac{10}{3}$$

The solution to the equation is $x = \frac{10}{3}$.

Comparing this to the given options:
(A) 3
(B) 4
(C) -1
(D) -3

It seems there might be a discrepancy between my calculated answer and the provided options, as $\frac{10}{3}$ is not among them. Let me re-check the calculation.

Re-checking Step 1:
$5 - 2(3x - 1) = -13$
$5 - 6x + 2 = -13$ (Correct)

Re-checking Step 2:
$7 - 6x = -13$ (Correct)

Re-checking Step 3:
$-6x = -13 - 7$
$-6x = -20$ (Correct)

Re-checking Step 4:
$x = \frac{-20}{-6}$
$x = \frac{10}{3}$ (Correct)

Since the calculated answer $\frac{10}{3}$ is not among the options (A) 3, (B) 4, (C) -1, (D) -3, there might be an error in the question's options or the question itself. However, if I were forced to choose the closest integer, none are particularly close.

Let's assume there might be a typo in the question or options. If the right side was, for example, -19:
$7 - 6x = -19$
$-6x = -26$
$x = 26/6 = 13/3$

If the right side was -11:
$7 - 6x = -11$
$-6x = -18$
$x = 3$ (Option A)

Let's assume the question intended for $x=3$ to be the answer and work backward to see what the right side of the equation would be.
If $x=3$:
$5 - 2(3(3) - 1)$
$5 - 2(9 - 1)$
$5 - 2(8)$
$5 - 16 = -11$
So, if the equation was $5 - 2(3x - 1) = -11$, then $x=3$ would be the correct answer.

Given the options, and the common practice in multiple-choice questions to have one correct answer, it's highly probable that the intended answer was $x=3$, and the right side of the equation was meant to be $-11$ instead of $-13$.

However, based on the exact question provided:

$$5 - 2(3x - 1) = -13$$

The correct solution is $x = \frac{10}{3}$. Since this is not an option, I cannot select one of the given choices.

If I must choose the closest integer option, $\frac{10}{3} \approx 3.33$. Option (A) is 3.

Given the constraint to select from the given options, and assuming a slight error in the problem statement or options, I will proceed with the assumption that $x=3$ was the intended answer, which would mean the equation should have been $5 - 2(3x - 1) = -11$.

If we strictly follow the given equation, none of the options are correct. However, if we consider the possibility of a typo in the constant on the right side, and that $x=3$ is an option, it's the most plausible intended answer.

Let's re-evaluate if there's any other interpretation. No, the steps are straightforward.

I will state the calculated answer and then address the options.

The final answer is $\boxed{x = \frac{10}{3}}$.

Based on the provided options, none of them match the calculated value of $x = \frac{10}{3}$. There might be an error in the question or the options. If the equation were $5 - 2(3x - 1) = -11$, then $x=3$ would be the correct answer, which is option (A).