Motivated by recent studies of supersymmetric black holes [1], we study the phase diagram of non-BPS \(AdS_5\) black holes [2] in the recently investigated four derivative effective action of five dimensional minimal gauged supergravity [3, 4]. In the sub critical electric potential limit, the phase diagrams show small and large black hole branches, with the latter undergoing a Hawking-Page (HP) transition [5]. Considering the four derivative ( \(\alpha \) ) corrections to be small, the non-BPS \(AdS_5\) black hole phase diagram remains intact. For temperatures below \(T_{HP}\) , \(\alpha \) corrections destabilise both small and large black holes; however, for temperatures above \(T_{HP}\) , they continue to destabilise the small black hole while stabilising the large one. In the critical electric potential limit, only large black holes exist with \(\alpha \) corrections stabilising them. In the maximum angular velocity limit, only small black holes exist, and \(\alpha \) corrections destabilise them.