  It is shown that the orbits of the space of local deformations of the Lie
algebra $\bar{A_5}$ over an algebraically closed field $K$ of characteristic 2
with respect to the automorphism group $\mathrm{PGL} (6)$ correspond to
$\mathrm{GL} (V)$-orbits of tri-vectors of a 6-dimensional space. For local
deformations corresponding to tri-vectors of rank $\rho <6$, integrability is
proved and global deformations are constructed.
