A group of office workers had some prize money to distribute among themselves. When all but one took $\$ 9$ each, the last person only received $\$ 5$. When they all took $\$ 8$ each, there was $\$ 12$ left over. How much had they won?

Step 1 ：Let's denote the total amount of prize money as \(T\) and the number of office workers as \(n\).

Step 2 ：From the first condition, we can form the equation \((n-1) \times 9 + 5 = T\). This means that when each person except one took $9, the remaining amount was $5.

Step 3 ：From the second condition, we can form the equation \(n \times 8 = T - 12\). This means that when each person took $8, there was $12 left.

Step 4 ：We can solve these two equations to find the values of \(T\) and \(n\).

Step 5 ：The solution to the system of equations gives us the total amount of prize money \(T\) and the number of office workers \(n\). According to the solution, the total amount of prize money is $140 and the number of office workers is 16.

Step 6 ：Final Answer: The office workers had won \(\boxed{140}\) dollars.