2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64243We prove that the space of mathematical instantons with second Chern class 5 over ${\mathbb P}_3$ is smooth and irreducible. Unified and simple proofs for the same statements in case of second Chern class $\leq 4$ are contained.corrections made, references added, 46 pages, Latex 2e. To appear in International Journal of MathematicsAlgebraic Geometry14D20Irreducibility and Smoothness of the moduli space of mathematical 5--instantons over ${\mathbb P}_3$text