To find the length between the points \( (2, 5) \) and \( (7, 3) \), we can use the distance formula, which is derived from the Pythagorean Theorem:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, let \( (x_1, y_1) = (2, 5) \) and \( (x_2, y_2) = (7, 3) \).
Now, substitute the values into the formula:
\[ d = \sqrt{(7 - 2)^2 + (3 - 5)^2} \] \[ d = \sqrt{(5)^2 + (-2)^2} \] \[ d = \sqrt{25 + 4} \] \[ d = \sqrt{29} \]
Now, we can calculate \( \sqrt{29} \):
\[ \sqrt{29} \approx 5.385 \]
Rounding this to the nearest hundredth gives:
\[ d \approx 5.39 \]
Thus, the length between the points \( (2, 5) \) and \( (7, 3) \) is approximately 5.39.