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 $Gal(E : F ) = \{ 1, \sigma \}.$ We write $\sigma(x) = \overline{x} \; \forall x \in E.$ Let $E^* := E \setminus \{ 0 \}$ and let $E^1 := \{x \in E \mid x \overline{x} = 1 \}$. $U(5)$ has three proper standard Levi subgroups, the minimal Levi subgroup $M_0 \cong E^* \times E^* \times E^1$ 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 $M_1.$ We describe - except several particular cases - the unitary dual in terms of Langlands-quotients.