To find the length between the points \((2, 5)\) and \((7, 3)\), we will use the Pythagorean theorem. The formula to calculate the distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, we have:
- \(x_1 = 2\)
- \(y_1 = 5\)
- \(x_2 = 7\)
- \(y_2 = 3\)
Now, substituting the values into the formula:
\[ d = \sqrt{(7 - 2)^2 + (3 - 5)^2} \]
Calculating the differences:
\[ d = \sqrt{(5)^2 + (-2)^2} \]
Calculating the squares:
\[ d = \sqrt{25 + 4} \]
Now, adding the squares:
\[ d = \sqrt{29} \]
Finally, calculating \(\sqrt{29}\):
\[ d \approx 5.385 \]
Rounded to the nearest hundredth, the distance is approximately:
\[ \boxed{5.39} \]