Numerical value of Derivative of Dirichlet L function at some particular points

I want to find the numerical value for the derivative of Dirichlet L function to compare with an another formula. However I am not able to obtain any numerical values. I tried to use

f[s_]= DirichletL[5,2,s] f'[3] 

But this simply returns DirichletL^(0,0,1)[5,2,3]. If I use N[f'[3]] this gives: DirichletL:: Positive integer expected at position 1 in DirichletL[5.,2.,2.].

Can someone please help me out with this? Any help is highly appreciated.