How many solutions does the equation \(5x + 3 = 5x + 8\) have?

To determine how many solutions the equation \(5x + 3 = 5x + 8\) has, we start by simplifying the equation. First, we can subtract \(5x\) from both sides: \[ 5x + 3 - 5x = 5x + 8 - 5x \] This simplifies to: \[ 3 = 8 \] The statement \(3 = 8\) is clearly false. Since we arrived at a contradiction, it indicates that there are no values of \(x\) that can satisfy the original equation. Thus, the equation \(5x + 3 = 5x + 8\) has no solutions. The final answer is: \[ \boxed{0} \]