5. Given that $f(x)$ and $g(x)$ are two quadratic functions with the leading coefficient of 1, if $g(6)=35, \frac{f(-1)}{g(-1)}=$ $\frac{f(1)}{g(1)}=\frac{21}{20}$, then $f(6)=$ $\qquad$ .
Let $h(x)=21 g(x)-20 f(x)$. According to the problem, $h(x)$ is a quadratic function with a quadratic coefficient of 1, and $h(-1)=h(1)=0$, so $h(x)=x^{2}-1$.
Therefore, $h(6)=21 g(6)-20 f(6)=35 \Rightarrow f(6)=35$.