Frist Campus Center is located $1$ mile north and $1$ mile west of Fine Hall. The area within $5$ miles of Fine Hall that is located north and east of Frist can be expressed in the form $\frac{a}{b} \pi - c$, where $a$, $b$, $c$ are positive integers and $a$ and $b$ are relatively prime. Find $a + b + c$.

Let's think step by step and output the final answer within \boxed{}.
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