$$ f ^ { \prime \prime } ( x ) = x [ \frac { - x } { ( x ^ { 2 } - 5 ) ^ { 3 } } ] + \frac { 1 } { \sqrt { x ^ { 2 } - 5 } } ( 1 ) $$

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To solve the given expression for $$ f^{\prime\prime}(x) $$, we need to simplify it step by step. The expression is:

$$
f^{\prime\prime}(x) = x \left[ \frac{-x}{(x^2 - 5)^3} \right] + \frac{1}{\sqrt{x^2 - 5}} (1)
$$

Let's break it down into two parts:

1. The first part: $$ x \left[ \frac{-x}{(x^2 - 5)^3} \right] $$
2. The second part: $$ \frac{1}{\sqrt{x^2 - 5}} $$

### Step 1: Simplifying the first part

The first part can be simplified as follows:

$$
x \left[ \frac{-x}{(x^2 - 5)^3} \right] = \frac{-x^2}{(x^2 - 5)^3}
$$

### Step 2: Simplifying the second part

The second part is already in a simplified form:

$$
\frac{1}{\sqrt{x^2 - 5}}
$$

### Step 3: Combining both parts

Now, we can combine both parts to get the final expression for $$ f^{\prime\prime}(x) $$:

$$
f^{\prime\prime}(x) = \frac{-x^2}{(x^2 - 5)^3} + \frac{1}{\sqrt{x^2 - 5}}
$$

### Final Expression

Thus, the simplified expression for $$ f^{\prime\prime}(x) $$ is:

$$
f^{\prime\prime}(x) = \frac{-x^2}{(x^2 - 5)^3} + \frac{1}{\sqrt{x^2 - 5}}
$$

If you need further analysis or specific evaluations, please let me know!
The simplified expression for $$ f^{\prime\prime}(x) $$ is: $$ f^{\prime\prime}(x) = \frac{-x^2}{(x^2 - 5)^3} + \frac{1}{\sqrt{x^2 - 5}} $$

\( f ^ { \prime \prime } ( x ) = x [ \frac { - x } { ( x ^ { 2 } - 5 ) ^ { 3 } } ] + \frac { 1 } { \sqrt { x ^ { 2 } - 5 } } ( 1 ) \)

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