Suppose that `f(x)` is a function of the form
`f(x)=(ax^(8)+bx^(6)+cx^(4)+dx^(2)+15x+1)/(x), (x ne 0)." If " f(5)=2`, then the value of `f(-5)` is _________.

Explanation

To solve the problem step by step, we start with the function given:

\[ f(x) = \frac{ax^8 + bx^6 + cx^4 + dx^2 + 15x + 1}{x}, \quad (x \neq 0) \]

### Step 1: Simplify the Function
We can simplify the function by dividing each term in the numerator by \( x \):

\[ f(x) = ax^7 + bx^5 + cx^3 + dx + 15 + \frac{1}{x} \]

### Step 2: Determine the Nature of the Function
Notice that the function consists of terms with odd powers of \( x \) (i.e., \( x^7, x^5, x^3, x \)) and a constant term \( 15 \) plus a term \( \frac{1}{x} \). The odd powers indicate that \( f(x) \) is an odd function.

### Step 3: Use the Property of Odd Functions
For odd functions, the property \( f(-x) = -f(x) \) holds. Therefore, we can express \( f(-x) \) as follows:

\[ f(-x) = -\left(ax^7 + bx^5 + cx^3 + dx + 15 + \frac{1}{x}\right) \]

This simplifies to:

\[ f(-x) = -ax^7 - bx^5 - cx^3 - dx - 15 - \frac{1}{x} \]

### Step 4: Find \( f(5) \)
We are given that \( f(5) = 2 \).

### Step 5: Set Up the Equation Using the Odd Function Property
Using the property of odd functions, we can set up the equation:

\[ f(5) + f(-5) = 30 \]

This is because \( f(5) + f(-5) = 15 + 15 = 30 \) (the constant terms).

### Step 6: Substitute the Known Value
Substituting \( f(5) = 2 \) into the equation gives:

\[ 2 + f(-5) = 30 \]

### Step 7: Solve for \( f(-5) \)
Now, we can solve for \( f(-5) \):

\[ f(-5) = 30 - 2 = 28 \]

### Final Answer
Thus, the value of \( f(-5) \) is:

\[ \boxed{28} \]