Graph the parabola.
\[
y=-(x+2)^{2}+3
\]

Plot five points on the parabola: the vertex, function button.

Step 1 ：First, we need to identify the vertex of the parabola. The vertex form of a parabola is given by \(y=a(x-h)^{2}+k\), where \((h,k)\) is the vertex of the parabola. In this case, the vertex is \((-2,3)\).

Step 2 ：Next, we need to find the y-intercept of the parabola. The y-intercept is the point where the parabola crosses the y-axis, which occurs when \(x=0\). Substituting \(x=0\) into the equation \(y=-(x+2)^{2}+3\), we get \(y=-1\). So, the y-intercept is \((0,-1)\).

Step 3 ：Finally, we can find two additional points on either side of the vertex by choosing arbitrary x-values and calculating the corresponding y-values. Let's choose \(x=-4\) and \(x=2\). Substituting these values into the equation, we get \(y=-1\) for both points. So, the additional points are \((-4,-1)\) and \((2,-1)\).

Step 4 ：\(\boxed{\text{Final Answer: The five points on the parabola are the vertex } (-2,3), \text{ the y-intercept } (0,-1), \text{ and three additional points } (-4,-1), (0,-1), \text{ and } (2,-1).}\)