In the early 2000 a series of geometric works, by Donaldson-Thomas and Tian in particular, have stimulated the analysis of Yang-Mills fields in dimension larger than the conformal one. We shall recall the main ingredients, developed mostly in the 80's, for the study of Yang-Mills Fields in critical and sub-critical dimensions. We will explain why most of these ingredients are inoperative in higher dimensions. The purpose of this talk is to present a new alternative framework for the calculus of variations of Yang-Mills Lagrangian in super-critical dimensions. This new framework will permit us to produce in particular minimizing Yang-Mills Fields with at most isolated point singularities for arbitrary boundary datas in 5 dimensional manifolds.