Explanation

Adding (3sinθ + 5cosθ)² = 25 and (5sinθ − 3cosθ)² = x² gives 34 = 25 + x², so x = ±3. At θ = 0 the given equation holds (3×0 + 5·1 = 5), forcing 5×0 − 3·1 = −3. Hence x = −3, option (a).