To determine if the table shows a proportional relationship between \( x \) and \( y \), we can check if the ratio \( \frac{y}{x} \) is constant for all pairs of \( (x, y) \).
Given the pairs:
- For \( (5, 25) \): \( \frac{25}{5} = 5 \)
- For \( (6, 30) \): \( \frac{30}{6} = 5 \)
- For \( (7, 35) \): \( \frac{35}{7} = 5 \)
- For \( (8, 40) \): \( \frac{40}{8} = 5 \)
Since the ratio \( \frac{y}{x} \) is consistently \( 5 \) for all pairs, the table does show a proportional relationship between \( x \) and \( y \).
So, the answer is: The table does show a proportional relationship between \( x \) and \( y \).