jmc

First we get rid of the fractions by multiplying both sides by 6. This gives us $$6\left(-\frac{2}{3}(x-5)\right)=6\left(\frac{3}{2}(x+1)\right),$$ so $$-4(x-5)=9(x+1).$$ Expanding both sides gives $-4x+20=9x+9$. Adding $4x$ to both sides and subtracting 9 from both sides gives $11=13x$, so $x=\boxed{\frac{11}{13}}$.