1. **State the problem:** Solve the equation $$-3r = \frac{5}{3}$$ for the variable $r$. 2. **Formula and rules:** To solve for $r$, we need to isolate $r$ on one side of the equation. Since $r$ is multiplied by $-3$, we divide both sides by $-3$. 3. **Isolate $r$:** $$r = \frac{\frac{5}{3}}{-3}$$ 4. **Simplify the division:** Dividing by $-3$ is the same as multiplying by $\frac{1}{-3}$: $$r = \frac{5}{3} \times \frac{1}{-3}$$ 5. **Multiply the fractions:** $$r = \frac{5 \times 1}{3 \times -3} = \frac{5}{-9}$$ 6. **Simplify the fraction:** $$r = -\frac{5}{9}$$ **Final answer:** $$r = -\frac{5}{9}$$