What Are The Coordinates Of The Vertex -x^+4x+5=0?

The x coordinate of the vertex of y = ax^2+bx+c is given by x=-b/(2a). For your equation, this is
x = -(4)/(2*-1) = -4/-2 = 2

The equation evaluated at x=2 is
y = -(2²) + 4(2) + 5
= -4+8+5
= 9

The coordinates of the vertex are (x, y) = (2, 9)