(х^2+5)*5*(х-1)(х+1)

To simplify the expression \((x^2+5) \cdot 5 \cdot (x-1)(x+1)\), we can follow these steps:

1. Recognize the structure: The expression can be broken down into parts:

   • \( (x^2 + 5) \) – a polynomial
   • \( 5 \) – a constant
   • \( (x-1)(x+1) \) – which is a difference of squares that simplifies to \( x^2 - 1 \)

2. Multiply the factors:

   First, expand \( (x-1)(x+1) \): \[ (x-1)(x+1) = x^2 - 1 \]

3. Combine everything: Now substituting this back into the expression: \[ (x^2 + 5) \cdot 5 \cdot (x^2 - 1) \]

4. Distribute the constant: Multiply \( 5 \) by \( (x^2 + 5) \): \[ 5(x^2 + 5) = 5x^2 + 25 \]

5. Final multiplication: Now multiply this by \( (x^2 - 1) \): \[ (5x^2 + 25)(x^2 - 1) \]

   This can be expanded as follows: \[ 5x^2 \cdot x^2 + 5x^2 \cdot (-1) + 25 \cdot x^2 + 25 \cdot (-1) \]

   Which results in: \[ 5x^4 - 5x^2 + 25x^2 - 25 \] Combining like terms: \[ 5x^4 + 20x^2 - 25 \]

So, the simplified form of the expression \((x^2 + 5) \cdot 5 \cdot (x-1)(x+1)\) is: \[ \boxed{5x^4 + 20x^2 - 25} \]