A quadratic function $y=f(x)$ is plotted on a graph and the vertex of the resulting parabola is $(4,-3)$. What is the vertex of the function defined as $g(x)=f(-x)+5$ ?

Step 1 ：A quadratic function $y=f(x)$ is plotted on a graph and the vertex of the resulting parabola is $(4,-3)$.

Step 2 ：The transformation $g(x)=f(-x)+5$ involves two operations: reflection in the y-axis and vertical translation.

Step 3 ：The reflection in the y-axis changes the sign of the x-coordinate of every point, including the vertex.

Step 4 ：The vertical translation moves every point up or down, changing the y-coordinate by the same amount for every point. In this case, the y-coordinate is increased by 5.

Step 5 ：Therefore, the vertex of $g(x)$ will be at $(-4, 2)$.

Step 6 ：Final Answer: The vertex of the function defined as $g(x)=f(-x)+5$ is \(\boxed{(-4, 2)}\).