Multiply and simplify $$ (x-4)\left(x^{2}+2 x+5\right) $$

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To multiply and simplify the expression $$(x - 4)\left(x^{2} + 2x + 5\right)$$, follow these steps:

1. **Distribute $$x$$ and $$-4$$ across the quadratic expression:**
   $$
   (x)(x^{2} + 2x + 5) - 4(x^{2} + 2x + 5)
   $$

2. **Multiply each term:**
   $$
   x \cdot x^{2} = x^{3}
   $$
   $$
   x \cdot 2x = 2x^{2}
   $$
   $$
   x \cdot 5 = 5x
   $$
   $$
   -4 \cdot x^{2} = -4x^{2}
   $$
   $$
   -4 \cdot 2x = -8x
   $$
   $$
   -4 \cdot 5 = -20
   $$

3. **Combine all the terms:**
   $$
   x^{3} + 2x^{2} + 5x - 4x^{2} - 8x - 20
   $$

4. **Combine like terms:**
   $$
   x^{3} + (2x^{2} - 4x^{2}) + (5x - 8x) - 20
   $$
   $$
   x^{3} - 2x^{2} - 3x - 20
   $$

**Final Simplified Expression:**
$$
x^{3} - 2x^{2} - 3x - 20
$$
$$ x^{3} - 2x^{2} - 3x - 20 $$

Multiply and simplify \( (x-4)\left(x^{2}+2 x+5\right) \)

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