1. **State the problem:** We need to find the range of the function $$g(x) = 4\sin\left(0.5(x+30)\right) - 5$$. 2. **Recall the range of sine function:** The sine function $$\sin(\theta)$$ has a range of $$[-1, 1]$$. 3. **Apply the transformation:** The function is scaled by 4 and shifted down by 5. So, $$g(x) = 4\sin\left(0.5(x+30)\right) - 5$$ 4. **Calculate the minimum value:** When $$\sin\left(0.5(x+30)\right) = -1$$, $$g(x) = 4(-1) - 5 = -4 - 5 = -9$$ 5. **Calculate the maximum value:** When $$\sin\left(0.5(x+30)\right) = 1$$, $$g(x) = 4(1) - 5 = 4 - 5 = -1$$ 6. **Conclusion:** The range of $$g(x)$$ is $$[-9, -1]$$.