Answer
$\sqrt{105}$.
Work Step by Step
We know that if $v=ai+bj+ck$ and $w=di+ej+fk$, then $v+w=(a+d)i+(b+e)j+(c+f)k$ and that if $z$ is a constant, then $zv=(za)i+(zb)j+(zc)k$.
Also, the magnitude of a vector $v=ai+bj+ck$ is: $||v||=\sqrt{a^2+b^2+c^2}$.
Hence here: $||v-w||=||(3i-5j+2k)-(-2i+3j-2k)||=||5i-8j+4k||=\sqrt{5^2+(-8)^2+4^2}=\sqrt{25+64+16}=\sqrt{105}$.