To determine the number of solutions for the equation
\[ \frac{15x - 5}{3} = 5x + 4, \]
we will first eliminate the fraction by multiplying both sides by 3:
\[ 15x - 5 = 3(5x + 4). \]
Now, distributing the 3 on the right side:
\[ 15x - 5 = 15x + 12. \]
Next, we will move all the terms involving \(x\) to one side and the constant terms to the other side. Subtract \(15x\) from both sides:
\[ 15x - 15x - 5 = 12, \]
which simplifies to:
\[ -5 = 12. \]
This statement is false, indicating that there are no values of \(x\) that can satisfy the original equation.
Thus, the conclusion is that the equation has no solutions. The correct answer is:
A) no solution.