If $\theta = 45^\circ$, then $v = \frac{5\sqrt{g}}{2}\ \text{ms}^{-1}$.

If $\theta = 45^\circ$, the particle reaches its maximum height before it reaches P.

If $\theta = 30^\circ$, the particle reaches its maximum height after reaching P.

If $\theta = \tan^{-1}\left(\frac{1}{5}\right)$, then $v = 125\sqrt{g}\ \text{ms}^{-1}$.