The correct statement that best shows how the vertical shift affects the parent function \( y = x \) when it is shifted to \( y = x + 5 \) is:
\( y = x + 5 \) will have each point 5 steps higher than \( y = x \).
This is because adding 5 to the function \( y = x \) raises the entire graph of the function vertically by 5 units.