jmc

Multiplying both sides by 2 and by 7 to eliminate fractions gives $$7(c-23)=2(2c+5).$$ Expanding both sides gives $7c-161=4c+10$. Subtracting $4c$ from both sides gives $3c-161=10$, and adding 161 to both sides gives $3c=171$. Finally, dividing by 3 gives $c=\frac{171}{3}=\boxed{57}$.