1. Stating the problem: We want to simplify the product $ (5 - x)(6 - 5x)(2 - x) $. 2. First, multiply the first two binomials: $$ (5 - x)(6 - 5x) = 5 \cdot 6 + 5 \cdot (-5x) - x \cdot 6 - x \cdot (-5x) = 30 - 25x - 6x + 5x^2 = 30 - 31x + 5x^2. $$ 3. Now multiply the result by the third binomial $(2 - x)$: $$ (30 - 31x + 5x^2)(2 - x). $$ 4. Distribute each term: $$ 30 \cdot 2 - 30 \cdot x - 31x \cdot 2 + 31x \cdot x + 5x^2 \cdot 2 - 5x^2 \cdot x $$ which simplifies to $$ 60 - 30x - 62x + 31x^2 + 10x^2 - 5x^3. $$ 5. Combine like terms: $$ 60 - 92x + 41x^2 - 5x^3. $$ 6. Therefore, the simplified expression is: $$ \boxed{ -5x^3 + 41x^2 - 92x + 60 }. $$