  In this paper we study the rank-one convex hull of a differential inclusion
associated to entropy solutions of a hyperbolic system of conservation laws.
This was introduced in Section 7 of [Kirchheim, M\"uller, \v{S}ver\'ak, 2003]
and many of its properties have already been shown in [Lorent, Peng,
2019]-[Lorent, Peng, 2020]. In particular, in [Lorent, Peng 2020] it is shown
that the differential inclusion does not contain any $T_4$ configurations. Here
we continue that study by showing that the differential inclusion does not
contain $T_5$ configurations.
