What is the vertex of f (x) = 5^2+20-16

The given equation is f (x) = 29. The graph is a horizontal line, which has no vertex. Perhaps you intend

... f (x) = 5x^2 + 20x - 16

... = 5 (x^2 + 4x + 4) - 16 - 20

... = 5 (x + 2) ^2 - 36

The vertex is (-2, - 36)