1. **State the problem:** Simplify $$\left( \frac{2p^5}{p^2} \right)^{-5}$$ with positive exponents. 2. **Apply the quotient rule for exponents:** $$\frac{p^5}{p^2} = p^{5-2} = p^3$$. So the expression becomes $$\left( 2p^3 \right)^{-5}$$. 3. **Apply the power of a product rule:** $$\left( 2p^3 \right)^{-5} = 2^{-5} \cdot (p^3)^{-5}$$. 4. **Apply the power of a power rule:** $$(p^3)^{-5} = p^{3 \times (-5)} = p^{-15}$$. So the expression is $$2^{-5} \cdot p^{-15}$$. 5. **Rewrite with positive exponents:** Negative exponents mean reciprocal, so $$2^{-5} = \frac{1}{2^5} = \frac{1}{32}$$ and $$p^{-15} = \frac{1}{p^{15}}$$. 6. **Combine the terms:** $$\frac{1}{32} \cdot \frac{1}{p^{15}} = \frac{1}{32p^{15}}$$. **Final answer:** $$\boxed{\frac{1}{32p^{15}}}$$