Use the remainder theorem and synthetic division to find $f(k)$. \[ f(k)=\square \] \[ k=-1 ; f(x)=x^{2}-2 x+5 \]

Step 1 ：The remainder theorem states that if a polynomial f(x) is divided by (x-k), then the remainder is f(k). In this case, we are asked to find f(k) for k=-1. We can use synthetic division to find the remainder when f(x) is divided by (x-(-1)) = (x+1). The remainder will be our f(k).

Step 2 ：Perform synthetic division with the dividend as [1, -2, 5] and the divisor as [1, 1].

Step 3 ：The remainder from the synthetic division is 8. According to the remainder theorem, this is the value of f(k) when k = -1.

Step 4 ：Final Answer: \(f(k)=\boxed{8}\)