To find the vertex you take half of the middle term and make it negative.
-4x is our middle term half of it is -2 and making it negative makes it +2
2 is our x value of the vertex
next you plug in 2 into the equation
2^2 -8 -5
4-8-5 = -9
Vertex is (2,-9)
Another way is a calculus way which is to take the derivative and set it equal to 0 then solve for x, to get your x value.