The nature of the bulk topological order of the 5/2 non-Abelian fractional quantum Hall state and the steady-state of its edge are long-studied questions. The most promising non-Abelian model bulk states are the Pfaffian (Pf), anti-Pffafian (APf), and particle-hole symmetric Pfaffian (PHPf). Here, we propose to employ a set of dc current-current correlations (electrical shot noise) in order to distinguish among the Pf, APf, and PHPf candidate states as well as to determine their edge thermal equilibration regimes: full vs partial. Using other tools, measurements of GaAs platforms have already indicated consistency with the PHPf state. Our protocol, realizable with available experimental tools, provides an only platform based on fully electrical measurements.