In　this　paper,　we　make　a　thorough　inquiry　about　the　Jacobi　stability　of　5D　self-exciting　homopolar　disc　dynamo　system　on　the　basis　of　differential　geometric　methods　namely　Kosambi-Cartan-Chern　theory.　The　Jacobi　stability　of　the　equilibria　under　specific　parameter　values　are　discussed　through　the　characteristic　value　of　the　matrix　of　second　KCC　invariants.　Periodic　orbit　is　proved　to　be　Jacobi　unstable.　Then　we　make　use　of　the　deviation　vector　to　analyze　the　trajectories　behaviors　in　the　neighborhood　of　the　equilibria.　Instability　exponent　is　applicable　for　predicting　the　onset　of　chaos　quantitatively.　In　addition,　we　also　consider　impulsive　control　problem　and　suppress　hidden　attractor　effectively　in　the　5D　self-exciting　homopolar　disc　dynamo.