\(\left(\dfrac{1}{3}-\dfrac{5}{6}\right)^2+\dfrac{5}{6}:2=\left(\dfrac{2}{6}-\dfrac{5}{6}\right)^2+\dfrac{5}{6}\times\dfrac{1}{2}=\left(\dfrac{-3}{6}\right)^2+\dfrac{5}{12}=\dfrac{1}{4}+\dfrac{5}{12}=\dfrac{3}{12}+\dfrac{5}{12}=\dfrac{8}{12}=\dfrac{2}{3}\)