1. **State the problem:** Solve the equation $$-\frac{59}{60} = -\frac{6}{5} + \frac{1}{5}k$$ for $k$. 2. **Isolate the term with $k$:** Add $\frac{6}{5}$ to both sides to move constants to one side: $$-\frac{59}{60} + \frac{6}{5} = \frac{1}{5}k$$ 3. **Find a common denominator to add fractions on the left:** The denominators are 60 and 5. Convert $\frac{6}{5}$ to sixtieths: $$\frac{6}{5} = \frac{6 \times 12}{5 \times 12} = \frac{72}{60}$$ 4. **Add the fractions:** $$-\frac{59}{60} + \frac{72}{60} = \frac{72 - 59}{60} = \frac{13}{60}$$ 5. **Rewrite the equation:** $$\frac{13}{60} = \frac{1}{5}k$$ 6. **Solve for $k$ by multiplying both sides by 5:** $$5 \times \frac{13}{60} = 5 \times \frac{1}{5}k$$ $$\frac{5 \times 13}{60} = \cancel{5} \times \frac{1}{\cancel{5}} k$$ $$\frac{65}{60} = k$$ 7. **Simplify the fraction:** $$\frac{65}{60} = \frac{13}{12}$$ **Final answer:** $$k = \frac{13}{12}$$