First lets convert 5 3/5 to improper fraction:
[tex]5\frac{3}{5}=\frac{5\cdot5+3}{5}=\frac{25+3}{5}=\frac{28}{5}[/tex]Now we can divide 28/5 by -1/2. Since we are dividing a positive number by a negative number, our answer will be negative:
[tex]\frac{\frac{28}{5}}{-\frac{1}{2}}=-\frac{28\cdot2}{5\cdot1}=-\frac{56}{5}=-11\frac{1}{5}[/tex]therefore, the final answer is -11 1/5