Another way to do it in AWK:
awk '/PATTERN/ {for(i=1; i<=5; i++) {getline; print}}' inputfile
in sed
:
sed -n '/PATTERN/{n;p;n;p;n;p;n;p;n;p}' inputfile
in GNU sed
:
sed -n '/PATTERN/,+7p' inputfile
or
sed -n '1{x;s/.*/####/;x};/PATTERN/{:a;n;p;x;s/.//;ta;q}' inputfile
The #
characters represent a counter. Use one fewer than the number of lines you want to output.