1. **State the problem:** Solve for $n$ in the equation $$-\frac{1}{5}n + 7 = 2$$. 2. **Isolate the term with $n$:** Subtract 7 from both sides: $$-\frac{1}{5}n + 7 - 7 = 2 - 7$$ $$-\frac{1}{5}n = -5$$ 3. **Solve for $n$:** Multiply both sides by the reciprocal of $-\frac{1}{5}$, which is $-5$: $$n = -5 \times (-5)$$ $$n = 25$$ 4. **Final answer:** The value of $n$ that satisfies the equation is $$\boxed{25}$$.