(-b/2a) = Vertex?
You are correct with your formula, we get -b/2a = 5/2
But we must take it one step further to find not the maximum value of x but the maximum value assumed by the function, meaning f(5/2).
f(5/2) = -(5/2)² + 5 * 5/2 - 4 = 9/4
Hope this helps!