First, we need to identify the form that this equation is in.
The given equation `y=3(x-2)^2+5` is in the form `y=a(x-h)^2+k`. This formula represents a parabolic function where `(h, k)` is the vertex and `x = h` is the axis of symmetry. The values: `h` represents a horizontal shift, `k` represents a vertical shift, and `a` affects the direction and the wideness of the parabola.
Now, let's identify the values of `h` and `k` from the given equation.
From `y=3(x-2)^2+5`, we see that `h` is `2` and `k` is `5`.
So, according to the standard function's form, our parabola will have the following properties:
* The axis of symmetry can be found using the equation `x = h`, substituting `h` gives us x = 2.
* The vertex of the equation is given by the coordinates `(h, k)`, substituting `h` and `k` gives us the point (2, 5).
In conclusion, for the given equation `y=3(x-2)^2+5`, the axis of symmetry is `x = 2`, and the vertex of the parabola is the point `(2, 5)`.