The first 5 years (from 1980 to 1985) of total solar irradiance observations by the first Active Cavity Radiometer Irradiance Monitor (ACRIM I) experiment on board the Solar Maximum Mission spacecraft show a clearly defined downward trend of -0.019% per year. The existence of this trend has been confirmed by the internal self-calibrations of ACRIM I, by independent measurements from sounding rockets and balloons, and by observations from the Nimbus-7 spacecraft. The trend appears to be due to unpredicted variations of solar luminosity on time scales of years, and it may be related to solar cycle magnetic activity.