The minimum dilatation of pseudo-Anosov 5-braids
  The minimum dilatation of pseudo-Anosov 5-braids is shown to be the largest zero $\lambda_5 \approx 1.72208$ of $x^4 - x^3 - x^2 - x + 1$ which is attained by $\sigma_1\sigma_2\sigma_3\sigma_4\sigma_1\sigma_2$. 
Ji-Young Ham, Won Taek Song