1. **State the problem:** Simplify the algebraic expression $5n + 4 - 8n + 7n - 5$. 2. **Combine like terms:** Group the terms with $n$ and the constant terms separately. $$5n - 8n + 7n + 4 - 5$$ 3. **Simplify the coefficients of $n$:** $$\cancel{5n} - \cancel{8n} + 7n = (5 - 8 + 7)n = 4n$$ 4. **Simplify the constants:** $$4 - 5 = -1$$ 5. **Write the simplified expression:** $$4n - 1$$ **Final answer:** $4n - 1$