1. **State the problem:** Simplify the expression $ (5 - 3i) - (-2 + 5i) $ where $ i = \sqrt{-1} $. 2. **Recall the rule:** Subtracting a complex number means subtracting both its real and imaginary parts. 3. **Apply the subtraction:** $$ (5 - 3i) - (-2 + 5i) = 5 - 3i + 2 - 5i $$ 4. **Combine like terms:** $$ (5 + 2) + (-3i - 5i) = 7 - 8i $$ 5. **Conclusion:** The expression simplifies to $ 7 - 8i $. **Final answer:** C) $7 - 8i$