First, we need to multiply each side of the equation by the common denominator of the two fractions. The common denominator is #8 xx 3 = color(red)(24)#

#5/8x xx color(red)(24) = -2/3 xx color(red)(24)#

#5/8x xx (color(red)(3 xx 8)) = -2/3 xx (color(red)(3 xx 8))#

#5/color(red)(cancel(color(black)(8)))x xx (color(red)(3 xx cancel(8))) = -2/color(red)(cancel(color(black)(3))) xx (color(red)(cancel(3) xx 8))#

#5x xx 3 = -2 xx 8#

#15x = -16#

Now, we divide each side of the equation by #color(red)(15)# to solve for #x#:

#(15x)/color(red)(15) = -16/color(red)(15)#

#(color(red)(cancel(color(black)(15)))x)/cancel(color(red)(15)) = -16/15#

#x = -16/15#