To determine which of the given options is a rational number between 5 and 514, let's analyze each option:
- \( \sqrt{26} \) ≈ 5.099 (irrational number)
- \( 525 \) is greater than 514 (not valid)
- \( 5 \frac{2}{5} \) = \( 5 + 0.4 = 5.4 \) (valid)
- \( 5 \frac{1}{7} \) = \( 5 + \frac{1}{7} \approx 5.142857 \) (valid)
- \( 513 \) is less than 514 but not between 5 and 514 (valid)
Now, let's summarize the valid options, which represent rational numbers between 5 and 514:
- \( 5 \frac{2}{5} \) (5.4)
- \( 5 \frac{1}{7} \) (approximately 5.142857)
Thus, both \( 5 \frac{2}{5} \) and \( 5 \frac{1}{7} \) are rational numbers validly between 5 and 514. However, the best answer would generally be the first one listed that matches the criteria.
So, the correct response from the given list would be:
5 Start Fraction 2 over 5 end fraction (which equals 5.4).