Summary: We find a new supersymmetric 5D solution of \(\mathcal N = 2\) supergravity coupled to one hypermultiplet that depends only on the fifth dimension (the energy scale in a holographic context). In one asymptotic limit the domain wall approaches to the \(AdS_{5}\) form but in the other one it does not. Similarly, the hyperscalars, which are all proportional between them, go asymptotically to a critical point of the potential only in one direction. The quaternionic Kähler manifold of the model is the \(H^{4}\) hyperboloid. We use the standard metric of \(H^{4}\) in an explicit conformally flat form with several arbitrary parameters. We argue that the holographic dual of the domain wall is a RG flow of a \(D = 4, \mathcal N = 1\) gauge theory acquiring a conformal supersymmetry at the IR limit, which corresponds to the \(AdS_{5}\) asymptotic limit.