  The aim of Reverse Mathematics(RM for short)is to find the minimal axioms
needed to prove a given theorem of ordinary mathematics. These minimal axioms
are almost always equivalent to the theorem, working over the base theory of
RM, a weak system of computable mathematics. The Big Five phenomenon of RM is
the observation that a large number of theorems from ordinary mathematics are
either provable in the base theory or equivalent to one of only four systems;
these five systems together are called the 'Big Five'. The aim of this paper is
to greatly extend the Big Five phenomenon as follows: there are two supposedly
fundamentally different approaches to RM where the main difference is whether
the language is restricted to second-order objects or if one allows third-order
objects. In this paper, we unite these two strands of RM by establishing
numerous equivalences involving the second-order Big Five systems on one hand,
and well-known third-order theorems from analysis about (possibly)
discontinuous functions on the other hand. We both study relatively tame
notions, like cadlag or Baire 1, and potentially wild ones, like
quasi-continuity. We also show that slight generalisations and variations of
the aforementioned third-order theorems fall far outside of the Big Five.
