Houston — With space shuttle ''Challenger'' nearly ready for its maiden flight next January, ''Discovery'' scheduled for completion in less than a year, and ''Atlantis'' headed for late 1984 delivery, the Space Transportation System (STS) is picking up speed. Columbia already has established an impressive 10.5 million-mile, 396-orbit track record in its first five space flights.
The milestones to date are:
* STS-1, April 12-14, 1981. John Young and Robert Crippen completed 36 earth orbits at a 166-mile altitude in a 54-hour mission that accomplished all 135 flight objectives.
* STS-2, Nov. 12-14, 1981. Joe Engle and Richard Truly completed 36 orbits at a 157-mile altitude after fuel-cell problems reduced the planned 124-hour mission to a 54-hour ''minimum mission.''
* STS-3, March 22-30, 1982. Jack Lousma and Gordon Fullerton completed 130 orbits at a 147-mile altitude after stretching their seven-day trip into eight days due to poor landing conditions on Day 7. The extended mission demonstrated Columbia'a flexibility and added to time for experiments.
* STS-4, June 27-July 4, 1982. Ken Mattingly and Henry Hartsfield completed 112 orbits at altitudes ranging from 184 to 197 miles in seven days. The mission marked the successful completion of the STS test phase, despite a design error that cost $36 million when the shuttle's rocket boosters sank before recovery.
* STS-5, Nov. 11-16, 1982. Vance Brand and Robert Overmyer were joined on the first operational STS flight by the first mission specialists, William Lenoir and Joseph Allen. They achieved the major objective of this 82-orbit, 185-mile high, five-day flight by launching two commercial satellites. Pressure-suit problems scrubbed a planned space walk but all else went as scheduled.