To solve this equation, we will first simplify by distributing the division operation:

X + 13 - (7x - 12)/3 = 5

Next, we will distribute the negative sign:

X + 13 - 7x/3 + 12/3 = 5

Simplify further:

X + 13 - 7x/3 + 4 = 5

Now, combine like terms:

X + 17 - 7x/3 = 5

Subtract 17 from both sides:

X - 7x/3 = -12

To eliminate the fraction, multiply through by 3:

3(X) - 7x = -36

3X - 7x = -36

Combine like terms:

-4X = -36

Divide by -4:

X = 9

Therefore, the solution to the equation is X = 9.