f(x)=1/3x^3-x^2+ax-5
f'(x)=x^2-2x+a=(x-1)^2+(a-1)>0或
f'(x)=x^2-x+a=(x-1)^2+(a-1)<0
x∈{-1,2},(x-1)^2∈{0,4}
为使f'(x)恒正,或恒负
应使a-1<-4或a-1>0
选D