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In this paper, we consider the Einstein-massive gravity coupled to theYang-Mills gauge field in five dimensions. Concentrating on the staticsolutions with planar horizon geometry, we explore the thermodynamic behaviorin the extended phase space and examine the validity of the first law ofthermodynamics besides local thermal stability by the Hessian matrix. Weobserve that although the topology of boundary is planar, there exists the vander Waals like phase transition for this kind of solution. We find the criticalquantities and discuss how the massive and Yang-Mills parameters affect them.Furthermore, some signatures of the first order phase transition such as theswallow-tail behavior of the Gibbs free energy and divergences of the specificheat are given in detail. We continue with the calculation of the photon sphereand the shadow observed by a distant observer. Finally, we use the WKB methodto investigate the quasinormal modes for scalar perturbation under changing themassive and Yang-Mills parameters.

Thermodynamics, shadow and quasinormal modes of black holes in five-dimensional Yang-Mills massive gravity