Solution:

The common difference is $-2y,$ so the third and fourth terms must be $x-3y$ and $x-5y.$ Thus $xy=x-3y$ and $\dfrac{x}{y}=x-5y.$

From $\dfrac{x}{y}=x-5y$ we get $x=xy-5y^2,$ and substituting $xy=x-3y$ gives $-3y-5y^2=0.$ Since $y\ne 0,$ $y=-\dfrac35$ and then $x=-\dfrac98.$

The fifth term is $x-7y=-\dfrac98 + \dfrac{21}{5}=\dfrac{123}{40}.$

Thus, the correct answer is E.