solution: 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 $2+8=\boxed{10}$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  What is the sum of the values of $a$ that satisfy the equation $$(3)5^2-4(5-a)^2 \div 3=63?$$
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 10
extra_info.question: What is the sum of the values of $a$ that satisfy the equation $$(3)5^2-4(5-a)^2 \div 3=63?$$
extra_info.split: test