1. The problem is to write the set $J = \{5, 10, 15, 20, 25\}$ in set builder notation. 2. Set builder notation describes a set by a property that its members satisfy. 3. We observe each element of $J$ is a multiple of 5. 4. The elements run from 5 to 25 increasing by 5, so we can define the set as $\{x \mid x = 5n, n \in \mathbb{N}, 1 \leq n \leq 5\}$. 5. Here $\mathbb{N}$ is the set of natural numbers, and $n$ runs from 1 to 5. 6. Therefore, the set builder notation is: $$J = \{x \mid x = 5n, n \in \mathbb{N}, 1 \leq n \leq 5\}.$$