1. **State the problem:** Evaluate the expression $$\frac{-8|5a^3 - 2ab| - b}{4a - b}$$ given $a = -1$ and $b = -3$.\n\n2. **Substitute the values:** Replace $a$ and $b$ in the expression:\n$$\frac{-8|5(-1)^3 - 2(-1)(-3)| - (-3)}{4(-1) - (-3)}$$\n\n3. **Calculate inside the absolute value:**\nCalculate $5(-1)^3 = 5 \times (-1) = -5$.\nCalculate $-2(-1)(-3) = -2 \times (-1) \times (-3) = -6$.\nSo inside the absolute value: $-5 - 6 = -11$.\n\n4. **Evaluate the absolute value:**\n$|-11| = 11$.\n\n5. **Calculate numerator:**\n$-8 \times 11 - (-3) = -88 + 3 = -85$.\n\n6. **Calculate denominator:**\n$4(-1) - (-3) = -4 + 3 = -1$.\n\n7. **Divide numerator by denominator:**\n$$\frac{-85}{-1} = 85$$\n\n**Final answer:** $85$