2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102041The minimum dilatation of pseudo-Anosov 5-braids is shown to be the largest zero $λ_5 \approx 1.72208$ of $x^4 - x^3 - x^2 - x + 1$ which is attained by $σ_1σ_2σ_3σ_4σ_1σ_2$.21 pages, 9 figures; a Mathematica script included in the source file as fbrmin.m and fbrmin.ps; one more section is added for describing implementation and some more subsections are added to IntroductionGeometric TopologyDynamical Systems37E30 (Primary); 37B40, 57M60 (Secondary)text