1. **State the problem:** Simplify the expression $\left(w^{-3}\right)^{-5}$. 2. **Recall the power of a power rule:** When raising a power to another power, multiply the exponents: $$\left(a^m\right)^n = a^{m \times n}$$ 3. **Apply the rule:** $$\left(w^{-3}\right)^{-5} = w^{-3 \times -5}$$ 4. **Multiply the exponents:** $$-3 \times -5 = 15$$ 5. **Simplify the expression:** $$w^{15}$$ 6. **Final answer:** The simplified form is $w^{15}$, which corresponds to option A.