f(x)=5√3cos^x+√3sin^x-4sinxcosx
=√3+2√3（1+cos2x)-2sin2x
=3√3+4cos(2x+π/6),
π/4<=x<=5π/12时,2π/3<2x+π/6<=π,f(x)是减函数；
5π/12∴f(x)的最小值=f(5π/12)=3√3-4.