Popov's nonconjugate Borel subgroups conjecture for the plane Cremona group

Let $n\geq 5$. The Cremona group ${\rm Bir}({\mathbb P}^n)$ is the group of birational transformations of complex projective $n$-space, and a Borel subgroup is a maximal closed connected solvable subgroup with respect to the Zariski topology. Popov's conjecture. For $n\geq 5$, ${\rm Bir}({\mathbb P}^n)$ contains nonconjugate Borel subgroups. This conjecture predicts that the standard Borel subgroup need not represent the unique conjugacy class in sufficiently high dimension; its status is not specified in the source.