Official solution
Given that x2 + y2 - 5x - y + 5 = 0
\[ \Rightarrow \] (x - 5/2)2 - \[{{25} \over 4}\] + (y - 1/2)2 - 1/4 = 0
\[ \Rightarrow \] (x - 5/2)2 + (y - 1/2)2 = 3/2
on circle [ Q \[ \equiv \] (5/2 + \[\sqrt {3/2} \] cos Q, \[{1 \over 2}\] + \[\sqrt {3/2} \] sin Q)]
\[ \Rightarrow \] PQ2 = \[{\left( {{5 \over 2} + \sqrt {3/2} \cos Q} \right)^2}\] + \[{\left( {{5 \over 2} + \sqrt {3/2} \sin Q} \right)^2}\]
\[ \Rightarrow \] PQ2 = \[{{25} \over 2} + {3 \over 2} + 5\sqrt {3/2} \] (cos Q + sinQ)
= 14 + 5\[\sqrt {3/2} \] (cosQ + sinQ)
\[ \therefore \] Maximum value of PQ2
= 14 + 5\[\sqrt {3/2} \] \[ \times \] \[\sqrt 2 \] = 14 + 5\[\sqrt 3 \]