Explanation:

- We have 5 consecutive odd numbers. Let them be: \(x, x+2, x+4, x+6, x+8\).

- The average of these numbers is given as 27.

- The formula for the average of numbers is: \(\frac{x + (x+2) + (x+4) + (x+6) + (x+8)}{5} = 27\).

- Simplifying: \(\frac{5x + 20}{5} = 27\).

- So, \(5x + 20 = 135\).

- Solving for \(x\): \(5x = 115\) ?\(x = 23\).

- Therefore, the numbers are: 23, 25, 27, 29, 31.

- The first and the last numbers are 23 and 31.

- Their product is: \(23 \times 31 = 713\).

- Thus, the correct option is Option 3: 713.