open LOGFILE, "<$file";
@lines = <LOGFILE>;
for my $i (0..$#lines) {
  next unless $lines[$i] =~ /$string_to_find/i;
  my $a = $i - 5 < 0 ? 0 : $i - 5;;
  my $b = $i + 5 > $#lines ? $#lines : $i + 5;
  print $lines[$_i] for my $_i ($a..$b);
}