Take out the factor 1/x on the left side: (1/x)(1-5/x)=(8/5)(1/x). The factor 1/x can be cancelled out on both sides leaving 1-5/x=8/5. Remove the fractions by multiplying through by 5x: 5x-25=8x; 3x=-25, so x=-25/3 or -(8 1/3). 1/x=-3/25.
Check in original equation: -3/25-5*9/625=-3/25-9/125=-(15+9)/125=-24/125=-(8*3)/(5*25). Right!