Let $z$ and $w$ be complex numbers such that $|z| = 2$ and $|w| = 5.$  Find the smallest possible value of $|w - z|.$
To find the smallest possible value of $|w - z|$, I need to minimize the distance between $z$ and $w$ in the complex plane. Since $|z| = 2$, $z$ lies on a circle of radius 2 centered at the origin. Similarly, since $|w| = 5$, $w$ lies on a circle of radius 5 centered at the origin. The distance between $z$ and $w$ is shortest when they lie on the same ray from the origin, and $w$ is farther from the origin than $z$. In that case, the distance $|w - z|$ is equal to the difference of their radii, $|w| - |z|$. So, the smallest possible value of $|w - z|$ is $5 - 2 = 3$.

