How do you find the axis of symmetry, and the maximum or minimum value of the function y=-3(x+2)^2+5?

AoS: $x = - 2$
Maximum: $y = 5$
The vertex form of a quadratic equation is $y = a {\left(x - b\right)}^{2} + c$ where $a$ is the amplitude (stretch/compress) and $\left(b , c\right)$ is the vertex of the parabola. The quadratic equation $y = - 3 {\left(x + 2\right)}^{2} + 5$ is in this form. Therefore, we can determine these features: the amplitude is $- 3$, and the coordinates of the vertex $\left(- 2 , 5\right)$. We can use this information to find the required attributes of the graph:
Axis of Symmetry AoS: $x = - 2$
Maximum/Minimum: $y = 5$ Since $a$ is negative, the graph opens downward, so this value is a maximum.