1. The problem is to simplify the expression $$\frac{(-a)^{41}}{a^5}$$. 2. We use the laws of exponents: $$\frac{x^m}{x^n} = x^{m-n}$$ and $$(-a)^n = (-1)^n a^n$$. 3. Apply the exponent rule to the denominator and numerator: $$\frac{(-a)^{41}}{a^5} = \frac{(-1)^{41} a^{41}}{a^5}$$. 4. Simplify the powers of $a$: $$= (-1)^{41} a^{41-5} = (-1)^{41} a^{36}$$. 5. Since 41 is odd, $$(-1)^{41} = -1$$, so the expression becomes: $$-a^{36}$$. Final answer: $$\boxed{-a^{36}}$$.