If 3 sin θ + 5 cos θ = 5, then what is the value of 5 sin θ - 3 cos θ?

Using the identity (3 sin θ + 5 cos θ)² + (5 sin θ - 3 cos θ)² = 9 + 25 = 34. So (5 sin θ - 3 cos θ)² = 34 - 25 = 9, giving 5 sin θ - 3 cos θ = ±3. Among the options, -3 is available.