Convert the equation
\[
f(x)=x^{2}-2 x-5
\]
into vertex form.

Step 1 ：Given the equation \(f(x) = x^2 - 2x - 5\)

Step 2 ：The vertex form of a quadratic equation is given by \(f(x) = a(x-h)^2 + k\), where \((h, k)\) is the vertex of the parabola.

Step 3 ：To convert the given equation into vertex form, we need to complete the square.

Step 4 ：The coefficient of \(x\) in the given equation is -2. Half of this value squared will give us the value we need to add and subtract inside the square to complete it. This value is \((-2/2)^2 = 1\).

Step 5 ：So, we can rewrite the equation as \(f(x) = (x^2 - 2x + 1) - 1 - 5\). This simplifies to \(f(x) = (x - 1)^2 - 6\).

Step 6 ：\(\boxed{The vertex form of the equation is (x - 1)^2 - 6}\)