To determine if \( \frac{5}{17} \) is a rational number between \( 5 \) and \( \frac{5}{14} \), we need to compare it with those two values.
First, we can convert \( 5 \) to a fraction: \( 5 = \frac{5}{1} \).
Next, we will approximate \( \frac{5}{14} \):
\[ \frac{5}{14} \approx 0.3571 \]
Now we convert \( \frac{5}{17} \):
\[ \frac{5}{17} \approx 0.2941 \]
Now we can clearly see the values:
- \( 5 \) is \( 5.0 \)
- \( \frac{5}{14} \approx 0.3571 \)
- \( \frac{5}{17} \approx 0.2941 \)
Since \( 0.2941 \) (which is \( \frac{5}{17} \)) is less than \( 0.3571 \) (which is \( \frac{5}{14} \)) and far less than \( 5 \), it is indeed not between \( 5 \) and \( \frac{5}{14} \).
Thus, the statement is False.