1. **State the problem:** Solve the equation $$\frac{x}{5} - \frac{2}{3} = 1$$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ on one side. We will first add $\frac{2}{3}$ to both sides to move constants to the right. 3. **Add $\frac{2}{3}$ to both sides:** $$\frac{x}{5} - \frac{2}{3} + \frac{2}{3} = 1 + \frac{2}{3}$$ $$\frac{x}{5} = 1 + \frac{2}{3}$$ 4. **Simplify the right side:** Convert 1 to a fraction with denominator 3: $$1 = \frac{3}{3}$$ So, $$\frac{x}{5} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3}$$ 5. **Isolate $x$ by multiplying both sides by 5:** $$5 \times \frac{x}{5} = 5 \times \frac{5}{3}$$ $$\cancel{5} \times \frac{x}{\cancel{5}} = \frac{25}{3}$$ $$x = \frac{25}{3}$$ 6. **Final answer:** $$x = \frac{25}{3}$$