smc

$f(x)$ is an odd function shifted down 5 units. Thus, it can be written as $f(x)=g(x)-5$ where $g(x)=a{x}^7+b{x}^3+cx$. Thus: $f(-7)=g(-7)-5=7$ and $g(-7)=12$. Using this and the fact $g(x)$ is odd, we can evaluate $f(7)$, which is: $$f(7)=g(7)-5=-g(-7)-5=-12-5=-17$$ Therefore, the answer is $\boxed{-17}$.