How can I make ‘grep’ show a single line five lines above the grepped line?

OK, I think this will do what you’re looking for. It will look for a pattern, and extract the 5th line before each match.

grep -B5 "pattern" filename | awk -F '\n' 'ln ~ /^$/ { ln = "matched"; print $1 } $1 ~ /^--$/ { ln = "" }'

basically how this works is it takes the first line, prints it, and then waits until it sees ^--$ (the match separator used by grep), and starts again.