  The kissing number $\tau(d)$ is the maximum number of pairwise
non-overlapping unit spheres each touching a central unit sphere in the
$d$-dimensional Euclidean space. In this note we report on how we discovered a
new, previously unknown arrangement of $40$ unit spheres in dimension $5$. Our
arrangement saturates the best known lower bound on $\tau(5)$, and refutes a
`belief' of Cohn--Jiao--Kumar--Torquato.
