In the latter part of the 1970's, the SR5 connotation denoted an option code for the HiLux series of trucks, similar to what the Z71 option code currently means for an upgraded Chevy or GMC pickup or Tahoe/Yukon.
Originally released around 1975, the 'S' denoted Sport, 'R' denoted the RN motor code, and '5' denoted the 5-speed transmission. It quickly caught on and the SR5 connotation passed onto the Corolla and then onto other Toyota car models.
Today, the SR5 generally denotes a specifc Toyota trim level, with a more sporty look and wide flexibility for options.
(Thanks to Dianne Whitmire at Carson Toyota and ToyotaOffRoad.com for the historial information.)