  In this paper, we will analyze a five-dimensional Yang-Mills black hole
solution in massive gravity's rainbow. We will also investigate the flow of
such a solution with scale. Then, we will discuss the scale dependence of the
thermodynamics for this black hole. Also, we study the criticality in the
extended phase space by treating the cosmological constant as the
thermodynamics pressure of this black hole solution. Moreover, we will use the
partition function for this solution to obtaining corrections to the
thermodynamics of this system and examine their key role on the behavior of
corrected solutions.
