1. Let the common difference of the arithmetic progression be d. Then, the fifth term is 3 + 4d = 9.
2. Solving for d, we get d = 1.5.
3. Let the number of terms in the progression be n. Then, the sum of the progression is \(\frac{n}{2}(2 \times 3 + (n - 1) \times 1.5) = 81\).
4. Simplifying further, we get \(3n + 0.75n(n - 1) = 81\).
5. Expanding the left side, we get \(3n + 0.75n^2 - 0.75n = 81\).
6. Combining like terms, we get \(0.75n^2 + 2.25n = 81\).
7. Dividing both sides by 0.75, we get \(n^2 + 3n = 108\).
8. Subtracting 108 from both sides, we get \(n^2 + 3n - 108 = 0\).
9. Factoring the left side, we get \((n + 12)(n - 9) = 0\).
10. Solving for n, we get n = -12 or n = 9.

So the correct answer is 9.