1. **State the problem:** Solve the equation $$\frac{x - 5}{7} = 40$$. 2. **Formula and rules:** To solve for $x$, multiply both sides of the equation by 7 to eliminate the denominator. 3. **Multiply both sides by 7:** $$7 \times \frac{x - 5}{7} = 7 \times 40$$ 4. **Cancel the 7 in the denominator and numerator:** $$\cancel{7} \times \frac{x - 5}{\cancel{7}} = 280$$ 5. **Simplify:** $$x - 5 = 280$$ 6. **Add 5 to both sides to isolate $x$:** $$x - 5 + 5 = 280 + 5$$ 7. **Simplify:** $$x = 285$$ **Final answer:** $$x = 285$$