Interaction energies of small model van der Waals fragments of group VA (P, As, Sb) and group VIA (S, Se, Te) are calculated using the complete basis set CCSD(T) method and compared to density functional results with approximate treatment of dispersion interaction using vdW-DF- and DFT-D-types of theories. These simple systems show surprising diversity of electronic properties ranging from more "metallic" to more "insulator" like, a property which needs to be captured in the approximate methods. While none of the standard approximate DFT theories provides an entirely satisfactory description of all the systems, we identify the most reliable approaches of each type. In addition, we show that results can be further tuned to chemical accuracy. In vdW-DF theory, guided by physical insights and the availability of quasi-exact CCSD(T) results, we supply the missing parts of correlation by matching an appropriate hybrid/semilocal exchange-correlation functional to describe short-/medium-range correlations accurately. In the DFT-D-type of theories, we reparametrize the empirical dispersion term. Since for such an accurate treatment benchmark calculations are needed, which typically is feasible only for a finite cluster, we argue that the cluster based model of the exchange-correlation hole is transferrable also to extended systems with vdW dispersion interactions.