The correct statement that best shows how the vertical shift affects the parent function \( y = x \) when shifted to \( y = x + 5 \) is:
"y=x+5 will have each point 5 steps higher than y=x."
This is because a vertical shift upwards by 5 units means that every point on the graph of the parent function \( y = x \) moves up by 5 units.