Let the equation `x^(5) + x^(3) + x^(2) + 2 = 0` has roots `x_(1), x_(2), x_(3), x_(4) and x_(5),` then find the value of `(x_(1)^(2)-1)(x_(2)^(2) - 1)(x_(3)^(2) - 1)(x_(4)^(2) - 1)(x_(5)^(2) - 1).`

Explanation

To solve the equation \( x^5 + x^3 + x^2 + 2 = 0 \) and find the value of \( (x_1^2 - 1)(x_2^2 - 1)(x_3^2 - 1)(x_4^2 - 1)(x_5^2 - 1) \), where \( x_1, x_2, x_3, x_4, x_5 \) are the roots of the equation, we can follow these steps:

### Step 1: Substitute \( x = 1 \)
We start by substituting \( x = 1 \) into the original equation:

\[ 1^5 + 1^3 + 1^2 + 2 = 1 + 1 + 1 + 2 = 5 \]

This gives us:

\[ 5 = (1 - x_1)(1 - x_2)(1 - x_3)(1 - x_4)(1 - x_5) \]

### Step 2: Substitute \( x = -1 \)
Next, we substitute \( x = -1 \) into the original equation:

\[ (-1)^5 + (-1)^3 + (-1)^2 + 2 = -1 - 1 + 1 + 2 = 1 \]

This gives us:

\[ 1 = (-1 - x_1)(-1 - x_2)(-1 - x_3)(-1 - x_4)(-1 - x_5) \]

Factoring out the negative signs, we have:

\[ 1 = (-1)(-1)(-1)(-1)(-1) \cdot (1 + x_1)(1 + x_2)(1 + x_3)(1 + x_4)(1 + x_5) \]

Thus:

\[ 1 = -(1 + x_1)(1 + x_2)(1 + x_3)(1 + x_4)(1 + x_5) \]

### Step 3: Set Up the Equations
From the above substitutions, we have two equations:

1. \( 5 = (1 - x_1)(1 - x_2)(1 - x_3)(1 - x_4)(1 - x_5) \)
2. \( 1 = -(1 + x_1)(1 + x_2)(1 + x_3)(1 + x_4)(1 + x_5) \)

### Step 4: Multiply the Two Equations
Now, we multiply both equations together:

\[ 5 \cdot 1 = (1 - x_1)(1 - x_2)(1 - x_3)(1 - x_4)(1 - x_5) \cdot -(1 + x_1)(1 + x_2)(1 + x_3)(1 + x_4)(1 + x_5) \]

This simplifies to:

\[ 5 = -[(1 - x_1)(1 + x_1)][(1 - x_2)(1 + x_2)][(1 - x_3)(1 + x_3)][(1 - x_4)(1 + x_4)][(1 - x_5)(1 + x_5)] \]

### Step 5: Recognize the Difference of Squares
Each term \( (1 - x_i)(1 + x_i) \) can be rewritten as \( 1 - x_i^2 \):

\[ 5 = -[(1 - x_1^2)(1 - x_2^2)(1 - x_3^2)(1 - x_4^2)(1 - x_5^2)] \]

### Step 6: Solve for the Desired Product
Thus, we have:

\[ -5 = (1 - x_1^2)(1 - x_2^2)(1 - x_3^2)(1 - x_4^2)(1 - x_5^2) \]

Taking the negative sign into account, we find:

\[ (x_1^2 - 1)(x_2^2 - 1)(x_3^2 - 1)(x_4^2 - 1)(x_5^2 - 1) = 5 \]

### Final Answer
Therefore, the value of \( (x_1^2 - 1)(x_2^2 - 1)(x_3^2 - 1)(x_4^2 - 1)(x_5^2 - 1) \) is:

\[ \boxed{5} \]