1. State the problem: Find the value of $k$ such that $5 - \frac{6}{k} = -13$. 2. Start by isolating the term with $k$: $$5 - \frac{6}{k} = -13$$ Subtract 5 from both sides: $$- \frac{6}{k} = -13 - 5$$ $$- \frac{6}{k} = -18$$ 3. Multiply both sides by $-1$ to make the left side positive: $$\frac{6}{k} = 18$$ 4. Solve for $k$ by multiplying both sides by $k$ and then dividing both sides by 18: $$6 = 18k$$ $$k = \frac{6}{18}$$ 5. Simplify the fraction: $$k = \frac{1}{3}$$ Final answer: $k = \frac{1}{3}$.