Edit: I managed to create a dummy file that printed according to what jayu_rao wanted, despite the double use of the counter noticed by hdb!

----original post below----

Are your caught lines not just too close together? Try adding the marker and counter that I put in below and look at the results. Also, if you make the match case insensitive you can compress the first three patterns into one. I tested it with the dummy file in the spoiler:

# dummy log file
.*Error.*1
stuff1
stuff2
.*Error.*2
stuff3
stuff4
stuff5
stuff6
stuff7
stuff8
stuff9
.*Error.*3
stuff10
.*Error.*4
stuff11
stuff12
stuff13
stuff14
stuff15
stuff16
stuff17
stuff18
stuff19
.*Error.*5
stuff20
stuff21
stuff22
stuff23
stuff24
stuff25
stuff26
[download]

#!/usr/bin/env perl
use strict;
use diagnostics;

open my $read_log, '<', '/home/jayu_rao/test_output/app.log' or die $!
+;
open my $write_tmp_app_log, '>', '/home/jayu_rao/test_output/write_tmp
+_app.log' or die $!;

my @patterns = (
  qr/.*Error.*/,
  qr/.*error.*/,
  qr/.*ERROR.*/,
  qr/.*FATAL.*/,
  qr/.*Critical.*/,
  qr/.*exception.*/,
);

my @lines=<$read_log>;
my $i;

my $counter=0;
for (@patterns){
for $i (0..$#lines) {
  next unless $lines[$i] =~ $_;
  my $a = $i - 5 < 0 ? 0 : $i - 5;;
  my $b = $i + 5 > $#lines ? $#lines : $i + 5;
  for $i($a..$b){
  print $write_tmp_app_log $lines[$i]
  };
  $counter++;
  print $write_tmp_app_log "----------marker$counter------------";
 }
}
close $read_log;
close $write_tmp_app_log;
[download]