5 Given that $x$ and $y$ are both negative integers satisfying the equation $y=\frac{10 x}{10-x}$, find the maximum value of $y$.
(A) -10
(B) -9
(C) -6
(D) -5
(E) None of the above
5 Answer: (D)
$$
y=\frac{10 x}{10-x} \Rightarrow x=10-\frac{100}{y+10}10 \Rightarrow-10<y<0 \text {. }
$$

Since both $x$ and $y$ are integers, $y+10$ is a factor of 100 , i.e. $y=-9,-8,-6,-5$. The maximum value of $y$ is -5 .