1. **State the problem:** Simplify the expression $$(-c)^{\frac{5}{3}}$$ assuming all variables are positive. 2. **Recall the rules:** For any positive variable $c$, and rational exponent $\frac{m}{n}$, we have $$a^{\frac{m}{n}} = \left(a^{\frac{1}{n}}\right)^m = \left(\sqrt[n]{a}\right)^m$$. 3. **Rewrite the expression:** Since $c$ is positive, we can write $$(-c)^{\frac{5}{3}} = (-1)^{\frac{5}{3}} \cdot c^{\frac{5}{3}}$$. 4. **Simplify $(-1)^{\frac{5}{3}}$:** $$(-1)^{\frac{5}{3}} = \left((-1)^5\right)^{\frac{1}{3}} = (-1)^{\frac{1}{3}}$$ The cube root of $-1$ is $-1$, so $$(-1)^{\frac{1}{3}} = -1$$. 5. **Combine results:** $$(-c)^{\frac{5}{3}} = -1 \cdot c^{\frac{5}{3}} = -c^{\frac{5}{3}}$$. 6. **Final answer:** $$\boxed{-c^{\frac{5}{3}}}$$