jmc

First we multiply all terms in the equation by 3 to avoid fractions and then solve for $a$. $$\begin{array}{rl}9\cdot 5^2-4(5-a{)}^2& =3\cdot 63\Rightarrow \\ -4(5-a{)}^2& =9\cdot 21-9\cdot 25\Rightarrow \\ & =9(-4)\Rightarrow \\ (5-a{)}^2& =9\end{array}$$ Therefore, $$\begin{array}{r}5-a=3\text{ OR }5-a=-3\Rightarrow \\ 2=a\text{ OR }8=a.\end{array}$$ The sum of the values of $a$ is $2+8=\boxed{10}$.