1. State the problem. Problem: Simplify the expression $ (5 + 5n^3) - (1 - 3n^3)$. 2. Formula and rules. Formula: $(a + b) - (c + d) = a + b - c - d$. Rule: To subtract polynomials, distribute the negative sign across the second parentheses and then combine like terms by adding coefficients of the same power of $n$. 3. Distribute the negative sign. $$ (5 + 5n^3) - (1 - 3n^3) = 5 + 5n^3 - 1 + 3n^3 $$. 4. Combine like terms and show intermediate grouping. $$5 + 5n^3 - 1 + 3n^3 = (5 - 1) + (5n^3 + 3n^3) $$. Evaluate the grouped sums. $$(5 - 1) = 4$$ $$(5n^3 + 3n^3) = 8n^3$$ 5. Final answer. $$8n^3 + 4$$ Therefore the simplified expression is $8n^3 + 4$.