Simplify $(1-i)^{5}$ and give your answer in rectangular form, polar form and exponential form.

Step 1 ：Express \( (1-i) \) in polar form: \( r = \sqrt{1^2 + (-1)^2} = \sqrt{2} \) and \( \theta = \arctan\left(\frac{-1}{1}\right) = -\frac{\pi}{4} \)

Step 2 ：Express \( (1-i) \) in exponential form: \( (1-i) = \sqrt{2}e^{-i\frac{\pi}{4}} \)

Step 3 ：Raise \( (1-i) \) to the power of 5: \( (1-i)^5 = \left(\sqrt{2}e^{-i\frac{\pi}{4}}\right)^5 \)

Step 4 ：Simplify the expression: \( (1-i)^5 = 2^{\frac{5}{2}}e^{-i\frac{5\pi}{4}} \)

Step 5 ：Convert back to rectangular form: \( (1-i)^5 = -4 + 4i \)

Step 6 ：Final Answer: In rectangular form, the simplified expression is \(\boxed{-4 + 4i}\). In polar form, it is \(\boxed{5.66\angle-225^\circ}\). In exponential form, it is \(\boxed{-4e^{i225^\circ}}\).