Step 1 :The functions $f$ and $g$ are defined as follows: $f(x)=-3 x-1$ and $g(x)=2 x^{2}-3 x$.
Step 2 :To find $f(7)$, we substitute $x$ with $7$ in the function $f(x)$, which gives us $f(7)=-22$.
Step 3 :To find $g(-5)$, we substitute $x$ with $-5$ in the function $g(x)$.
Step 4 :After substituting, we get $g(-5) = 65$.
Step 5 :So, the final answers are $f(7) = -22$ and $g(-5) = \boxed{65}$.