Two sides of a triangle are given by the roots of the equation $x^2-5x+6=0$ and the angle between the sides is $\large\frac{\pi}{3}$. Then the perimeter of the triangle is :

Question

$$\begin {array} {1 1} (a)\;5 +\sqrt 2 & \quad (b)\;5+\sqrt 3 \\ (c)\;5+\sqrt 5 & \quad (d)\;5+\sqrt 7 \end {array}$$