①f(3)=-9+3a+b,
f'(x)=x^2-4x+a,
f'(3)=-3+a,
曲线y=f(x)在(3,3a+b-9)处的切线方程是y=3x+5,
∴a-3=3,a=6,
b+9=14,b=5.
②f(x)=(1/3)x^2-2x^2+6x+5,
g(x)=f(x)+m/(x+2)在[3,+∞)上是增函数,
∴g'(x)=x^2-4x+6-m/(x+2)^2>=0对x>=3恒成立,
∴m=3,
h'(x)=(2x-4)(x+2)^2+2(x^2-4x+6)(x+2)
=2(x+2)(2x^2-4x+2)
=4(x+2)(x-1)^2>0,
∴h(x)是增函数,h(x)>=h(3)=75,
∴m的最大值=75.