1. The problem asks us to find the union of the two sets $A$ and $B$, where $A = \{3, 5, 6, 8, 9\}$ and $B = \{2, 3, 4, 5\}$. 2. The union of two sets $A$ and $B$, denoted by $A \cup B$, is the set containing all the elements from both sets without duplicating elements. 3. Combine the elements of $A$ and $B$: $\{3, 5, 6, 8, 9\} \cup \{2, 3, 4, 5\}$. 4. Remove duplicates to list each element only once: $\{2, 3, 4, 5, 6, 8, 9\}$. 5. Thus, the union $A \cup B = \{2, 3, 4, 5, 6, 8, 9\}$.