this is one of the way. try this

#!/usr/bin/env perl

use strict;

my $hits=0;
my $string_to_find="string";
my $file = "filename";

open   (LOGFILE, $file);
my @cont = <LOGFILE>;
close(LOGFILE);

for(my $i = 0; $i <= $#cont; $i++) {
my $line = $cont[$i];

if ($line =~ /$string_to_find/i) {
  my $st;
  ($i <= 5) ? ($st = 0) : ($st = $i - 5);
  my $ln = $i - 1;

  my $eln = $i + 1;
  my $en = $i + 5;
  ($en > $#cont) ? ($en = $#cont) : ();

  print @cont[$st..$ln];
  print $line;
  print @cont[$eln..$en];

}
}
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