In the perfect T-shaped pi-pi stacking between to benzenes the distance is around 3.8 Angstroms (http://pubs.acs.org/doi/abs/10.1021/ja049434a). I would say that 5 Angstroms could be possible for a subtle interactions, depending on how you define the distance.
If we really are talking about center-to-center distances of interacting aromatic moieties, distances of around 5 Å are actually what is usually found experimentally. See for instance S. K. Burley, G. A. Petsko, Science 1985, 229, 23–28. (https://www.ncbi.nlm.nih.gov/pubmed/3892686 ), or table 2 in https://www.ncbi.nlm.nih.gov/pubmed/24401011 .