Step 1 :Given that 2 is a zero of the polynomial function \(f(x) = x^{3} - 10x^{2} + 36x - 40\), we can find the remaining zeros by dividing the polynomial by \((x - 2)\).
Step 2 :The quotient polynomial is then \(x^{2} - 8x + 20\).
Step 3 :We find the zeros of this polynomial by setting it equal to zero and solving for \(x\).
Step 4 :Solving \(x^{2} - 8x + 20 = 0\) gives us the remaining zeros of the original polynomial.
Step 5 :Final Answer: The remaining zeros of the polynomial function \(f(x) = x^{3} - 10x^{2} + 36x - 40\) are \(\boxed{4, 5}\).