More information is needed, but from 1977-1981, the standard race distance for HS XC was 2.5 miles. At least that was the distance contested during the tournament. 5k became the standard distance in 1982.
What was the time displayed on your records board?
Feel free to PM me the runner's name and school, and I might be able to dig something up for you.
Maybe the runner had an opportunity to run a 5k somewhere during the year, but my initial reaction is that perhaps somebody extrapolated the runner's 5k time based on a 2.5 mile performance, as ridiculous and unconventional as that may seem.