When f(x) = ax^3 - 6x^2 + bx - 5 is divided by x - 1, the remainder is 5. When f(x) is divided by x - 2, the remainder is -53. Find the ordered pair (a,b).

By remainder theorem, we get \(\begin{cases} f(1) = 5\\ f(2) = -53 \end{cases}\).

Now, using the definition of f(x), we have a system of linear equations in a and b. Can you take it from here?