Unitary Dual of p-adic U(5)

We study the parabolically induced complex representations of the unitary group in 5 variables, $U(5),$ defined over a p-adic field. Let $F$ be a p-adic field. Let $E:F$ be a field extension of degree two. Let $Gal(E : F ) = { 1, \sigma }.$Wewrite$ \sigma(x) = \overline{x} ; \forall x \in E. $Let$ E^* := E \setminus { 0 } $andlet$ E^1 := {x \in E \mid x \overline{x} = 1 }$\mathrm{.}$U(5) $ has three proper standard Levi subgroups, the minimal Levi subgroup $M_0\cong E^{\ast }\times E^{\ast }\times E^1$ and the two maximal Levi subgroups $M_1\cong GL(2,E)\times E^1$ and $ M_2 \cong E^* \times U(3)$. We consider representations induced from the minimal Levi subgroup $M_0,$ representations induced from non-cuspidal, not fully-induced representations of the two maximal Levi subgroups $M_1$ and $M_2,$ and representations induced from cuspidal representations of $M_1\mathrm{.}$ We describe - except several particular cases - the unitary dual in terms of Langlands-quotients.