Tree Diameter - Problem Statement

The diameter of a tree is the length of the longest path between any two nodes. The path can start and end anywhere. Example: In a tree with edges $1$-$2$, $2$-$3$, $2$-$4$, $4$-$5$, the diameter is $3$.

The longest path is $3 \to 2 \to 4 \to 5$ (or $1 \to 2 \to 4 \to 5$). Before reading on, think about this: the longest path either stays entirely in one subtree, or it passes through some node connecting two subtrees. How would you use this?