The distance of the point $Q(0,2,-2)$ from the line passing through the point $P(5,-4,3)$ and perpendicular to the lines $\ \vec r = (-3\hat i + 2\hat k) + \lambda(2\hat i + 3\hat j + 5\hat k),\ \lambda\in\mathbb R,$ and $\ \vec r = (\hat i - 2\hat j + \hat k) + \mu(-\hat i + 3\hat j + 2\hat k),\ \mu\in\mathbb R,$ is: