$$(x-3{)}^2=8(y-5)$$
vertex:
focus :
directrix"

Step 1 ：The given equation is in the form of a parabola. The standard form of a parabola is $(x-h{)}^2=4a(y-k)$ for a parabola that opens upwards or downwards, and $(y-k{)}^2=4a(x-h)$ for a parabola that opens to the left or right. Here, the given equation is in the form of $(x-h{)}^2=4a(y-k)$, which means the parabola opens upwards or downwards.

Step 2 ：The vertex of the parabola is given by the point (h, k). In this case, h = 3 and k = 5, so the vertex is (3, 5).

Step 3 ：The focus of the parabola is given by the point (h, k + a), where a is the distance from the vertex to the focus. In this case, we can find a by comparing the given equation with the standard form of the parabola. We have 4a = 8, so a = 2. Therefore, the focus is (3, 5 + 2) = (3, 7).

Step 4 ：The directrix of the parabola is the line y = k - a. In this case, the directrix is y = 5 - 2 = 3.

Step 5 ：Final Answer: The vertex of the parabola is $\boxed{{\displaystyle (3,5)}}$, the focus is $\boxed{{\displaystyle (3,7)}}$, and the directrix is $\boxed{{\displaystyle y=3}}$.