Given the Quadratic Function:
[tex]f\mleft(x\mright)=5\mleft(x+1\mright)^2-3[/tex]
You can identify that is written in Vertex Form.
By definition, the Vertex Form of a Quadratic Function is:
[tex]f(x)=a(x-h)^2+k[/tex]
Where the vertex of the parabola is:
[tex](h,k)[/tex]
In this case, you can identify that:
[tex]\begin{gathered} h=-1 \\ k=-3 \end{gathered}[/tex]
Therefore, the answer is:
[tex](-1,-3)[/tex]
