Vertex form uses the following formula:
[tex]y = a(x-h)^2 + k[/tex]
Identify the values of h and k in your function:
[tex](x+5)^2 - 28[/tex]
[tex]h = -5, k = -28[/tex]
The vertex is found with the following point:
[tex](h,k)[/tex]
[tex]\text{Vertex: (-5, -28)}[/tex]
The vertex will be found at (-5, -28).