The radius of a circle is the distance from the center of the circle to any point on the circle. We can use the distance formula to find the distance between the points (2, 3) and (5, 7): \begin{align*} \sqrt{(5-2)^2 + (7-3)^2} &= \sqrt{3^2 + 4^2} \\ &= \sqrt{9+16} \\ &= \sqrt{25} \\ &= 5 \end{align*} The radius of the circle is 5 units.