You don't have to use the power rule for negative powers, you can use the quotient rule: -5/3x= f(x)/g(x) with f(x)= -5 and g(x)= 3x.
(f/g)'= (f'g- fg')(g2)
Since f'= 0 and g'= 3, that gives (-5/3x)'= ((0)(3x)- (-5)(3))/(9x2= 5/3x2.
The reason I mention that is that before you can use the power rule for negative powers you have to prove it for negative powers- and you do that by using the quotient rule:
x-n= 1/xn= f/g with f(x)= 1, g(x)= xn. f'= 0, g'= nxn-1 so (x-n)'= (1/xn)'= ((0)(xn)- 1(nxn-1)/x2n= n xn-1/x2n= n x(n-1)- 2n= n x-n-1.