A shopper buys a $100$ dollar coat on sale for $20\%$ off.  An additional $5$ dollars are taken off the sale price by using a discount coupon.  A sales tax of $8\%$ is paid on the final selling price.  The total amount the shopper pays for the coat is
$\text{(A)}\ \text{81.00 dollars} \qquad \text{(B)}\ \text{81.40 dollars} \qquad \text{(C)}\ \text{82.00 dollars} \qquad \text{(D)}\ \text{82.08 dollars} \qquad \text{(E)}\ \text{82.40 dollars}$
After the $20\%$ sale, the coat costs $100(0.8)=80$ dollars. Then $5$ dollars are taken off for a cost of $80-5=75$. Adding on the sales tax, the final amount is $(75)(1.08)=\boxed{\text{(A)}\ 81.00\ \text{dollars}}$.