Until the late 1980s, phases of matter were understood in terms of Landau's symmetry breaking theory. Following the discovery of the quantum Hall effect the introduction of a second class of phases, those with topological order, was necessary. Phase transitions within the first class of phases involve a change in symmetry, whereas those between topological phases require a change in topological order. However, in rare cases transitions may occur between the two classes in which the vanishing of the topological order is accompanied by the emergence of a broken symmetry. Here, we report the existence of such a transition in the two-dimensional electron gas. When tuned by hydrostatic pressure, the ν = 5/2 fractional quantum Hall state, believed to be a prototype non-Abelian topological phase, gives way to a quantum Hall nematic phase. Remarkably, this nematic phase develops spontaneously, i.e. in the absence of any externally applied symmetry breaking fields.