a) $f(x)=x^{2}-6 x+5$ b) $f(x)=3 x^{2}-4 x$ c) $f(x)=x^{2}-9$ d) $f(x)=-6 x^{2}$ e) $f(x)=x^{2}-7 x+10$

Step 1 ：Calculate the x-coordinate of the vertex for each function using the formula \(x = -\frac{b}{2a}\).

Step 2 ：Plug the x-coordinate back into the function to find the y-coordinate of the vertex.

Step 3 ：\(\boxed{\text{a) The vertex of } f(x) = x^2 - 6x + 5 \text{ is } (3.0, -4.0)}\)

Step 4 ：\(\boxed{\text{b) The vertex of } f(x) = 3x^2 - 4x \text{ is } (0.6666666666666666, -1.3333333333333333)}\)

Step 5 ：\(\boxed{\text{c) The vertex of } f(x) = x^2 - 9 \text{ is } (0.0, -9.0)}\)

Step 6 ：\(\boxed{\text{d) The vertex of } f(x) = -6x^2 \text{ is } (0.0, 0.0)}\)

Step 7 ：\(\boxed{\text{e) The vertex of } f(x) = x^2 - 7x + 10 \text{ is } (3.5, -2.25)}\)