1. The problem asks to find the symmetric difference $A \Delta B$ where $A = \{1, 2, 5\}$ and $B = \{2, 3, 5\}$. 2. The symmetric difference of two sets $A$ and $B$ is defined as the set of elements which are in either of the sets and not in their intersection. Mathematically, $$A \Delta B = (A \cup B) \setminus (A \cap B)$$ 3. First, find the union $A \cup B$: $$A \cup B = \{1, 2, 3, 5\}$$ 4. Next, find the intersection $A \cap B$: $$A \cap B = \{2, 5\}$$ 5. Now, subtract the intersection from the union to get the symmetric difference: $$A \Delta B = \{1, 2, 3, 5\} \setminus \{2, 5\} = \{1, 3\}$$ 6. Therefore, the symmetric difference $A \Delta B$ is $\{1, 3\}$.