Synthesis of high-entropy alloys often involves heating precursors to above 1000 °C such that entropy stabilization takes effect. The resulting alloys are characterized by random element distribution at the bulk lattice positions. Surfaces may however be more ordered, even at high temperatures. We explore the local order at (111), (100), and (533) surfaces of the equimolar face-centered cubic (fcc) AgAuCuPdPt high-entropy alloy at high temperatures and thermal equilibrium. We find that the local order is significantly increased at the (100) surface and to a lesser extent at the (533) and (111) surfaces compared to bulk AgAuCuPdPt. The (100) surface both segregates with increased amounts of Au and Ag and less Pd and Pt and has a more ordered distribution of nearest-neighbor atom pairs. The (111) surface segregates with increased amounts of Au and Ag and less Cu, Pd, and Pt, but the nearest-neighbor distribution is mostly random. The (100)-type step edge of the (533) surface resembles the (100) surface. The degree of surface order seems linked to the structure ensemble's energy distribution width, so we suggest that the width can be used to estimate the degree of order in high-entropy alloys with minimal computational efforts.