To find the distance between the points \( (2, 5) \) and \( (7, 3) \), we can use the distance formula, which is derived from the Pythagorean theorem. The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Substituting the coordinates of the points into the formula:
- \( (x_1, y_1) = (2, 5) \)
- \( (x_2, y_2) = (7, 3) \)
We calculate:
\[ d = \sqrt{(7 - 2)^2 + (3 - 5)^2} \]
Calculating the differences:
\[ d = \sqrt{(5)^2 + (-2)^2} \]
Now, squaring the differences:
\[ d = \sqrt{25 + 4} = \sqrt{29} \]
Now, we need to find the approximate value of \( \sqrt{29} \). Calculating \( \sqrt{29} \):
\[ \sqrt{29} \approx 5.385 \]
Rounding to the nearest hundredth:
\[ \sqrt{29} \approx 5.39 \]
Thus, the length between the points \( (2, 5) \) and \( (7, 3) \) is approximately \( \boxed{5.39} \).