We present results of a high-frequency all-sky search for continuous gravitational waves from isolated compact objects in LIGO's fifth science run (S5) data, using the computing power of the Einstein@Home volunteer computing project. This is the only dedicated continuous gravitational wave search that probes this high-frequency range on S5 data. We find no significant candidate signal, so we set 90% confidence level upper limits on continuous gravitational wave strain amplitudes. At the lower end of the search frequency range, around 1250 Hz, the most constraining upper limit is 5.0×10-24, while at the higher end, around 1500 Hz, it is 6.2×10-24. Based on these upper limits, and assuming a fiducial value of the principal moment of inertia of 1038 kg m2, we can exclude objects with ellipticities higher than roughly 2.8×10-7 within 100 pc of Earth with rotation periods between 1.3 and 1.6 milliseconds.