What is the sum of the values of $a$ that satisfy the equation $$(3)5^2-4(5-a)^2 \div 3=63?$$
First we multiply all terms in the equation by 3 to avoid fractions and then solve for $a$. \begin{align*}
9\cdot5^2-4(5-a)^2&=3\cdot63\quad\Rightarrow\\
-4(5-a)^2&=9\cdot21-9\cdot25\quad\Rightarrow\\
&=9(-4)\quad\Rightarrow\\
(5-a)^2&=9
\end{align*} Therefore, \begin{align*}
5-a=3\quad\text{ OR }\quad 5-a=-3\quad\Rightarrow\\
2=a \quad\text{ OR }\quad 8=a.
\end{align*} The sum of the values of $a$ is $2+8=\boxed{10}$.