1. **State the problem:** Solve the equation $$\frac{1}{5}(x - 5) = 7$$ for $x$. 2. **Formula and rules:** To solve for $x$, first eliminate the fraction by multiplying both sides by 5. Then isolate $x$ by adding or subtracting terms. 3. **Multiply both sides by 5:** $$5 \times \frac{1}{5}(x - 5) = 5 \times 7$$ $$\cancel{5} \times \frac{1}{\cancel{5}}(x - 5) = 35$$ $$x - 5 = 35$$ 4. **Add 5 to both sides to isolate $x$:** $$x - 5 + 5 = 35 + 5$$ $$x = 40$$ 5. **Final answer:** $$\boxed{40}$$