f(x)=2cosxsin(x+π/3)-√3sin²x+sinxcosx
=2cosx(1/2*sinx+√3/2*cosx) -√3sin²x+sinxcosx
= sinxcosx+√3cos²x-√3sin²x+sinxcosx
=2 sinxcosx+√3(cos²x-sin²x)
=sin2x+√3cos2x
=2sin(2x+π/3)
(1)
最小正周期=2π/2=π
（2）
x∈[0,5π/12]
2x+π/3∈[π/3,7π/6]
sin(2x+π/3)∈[-1/2,1]
2sin(2x+π/3)∈[-1,2]
f（x）＞m成立
m