We present observations of an anisotropic resistance state at Landau-level filling factor nu = 5/2 in a two-dimensional hole system (2DHS), which occurs for certain values of hole density p and average out-of-plane electric field E-perpendicular to. The 2DHS is induced by electric-field effect in an undoped GaAs/AlGaAs quantum well, where front and back gates allow independent tuning of p and E-perpendicular to, and hence the symmetry of the confining potential. For p approximate to 2 x 10(11 )cm(-2) and E-perpendicular to approximate to -2 x 10(5) V/m, the magnetoresistance along < 01 (1 >) over bar greatly exceeds that along < 011 >, suggesting the formation of a quantum Hall nematic or "stripe" phase. Reversing the sign of E-perpendicular to rotates the stripes by 90 degrees. We suggest this behavior may arise from the mixing of the hole Landau levels and a combination of the Rashba and Dresselhaus spin-orbit coupling effects.