jmc

By the Triangle Inequality, $$|w|=|(w-z)+z|\le |w-z|+|z|,$$so $|w-z|\le |w|-|z|=5-2=3.$

We can achieve this bound by taking $w=5$ and $z=2,$ so the smallest possible value is $\boxed{3}.$



Geometrically, $z$ lies on the circle centered at the origin with radius 2, and $w$ lies on the circle centered at the origin with radius 5. We want to minimize the distance between $w$ and $z$; geometrically, it is clear that the minimum distance is 3.