Observations of cosmic-ray electrons and positrons have been made with a new balloon-borne detector , HEAT ( the “ High-Energy Antimatter Telescope ” ) , first flown in 1994 May from Fort Sumner , NM . We describe the instrumental approach and the data analysis procedures , and we present results from this flight . The measurement has provided a new determination of the individual energy spectra of electrons and positrons from 5 GeV to about 50 GeV , and of the combined “ all-electron ” intensity { ( e ^ { + } + e ^ { - } ) } up to \sim 100 GeV . The single power-law spectral indices for electrons and positrons are \alpha = 3.09 \pm 0.08 and 3.3 \pm 0.2 , respectively . We find that a contribution from primary sources to the positron intensity in this energy region , if it exists , must be quite small .