If I've understood correctly, you could construct a hash keyed by the four columns of interest. If you split the line on whitespace and slice out the columns and join them again with some delimiter (I chose a colon) you construct the key. I have added a line to your "array 2" data with a common "bold part" so you can see that it gets removed.

Note that I have used Data::Dumper so that you can see the lookup hash and resultant @array2. Here's the code.

use strict;
use warnings;

use Data::Dumper;

open my $array1FH, q{<}, \ <<'EOF1' or die qq{open: < HEREDOC 1: $!\n}
+;
ATOM   2198  SG  CYS L  51      39.781 -12.827   5.691  1.00 26.67
ATOM   2199  N   MET L  52      37.845 -15.766   5.722  1.00 33.08
ATOM   2200  CA  MET L  52      38.312 -17.144   5.674  1.00 33.08
ATOM   2201  C   MET L  52      37.329 -18.022   4.901  1.00 33.08
EOF1

my @array1 = <$array1FH>;
close $array1FH or die qq{close: < HEREDOC 1: $!\n};

my %array1Lookup =
   map { join( q{:}, ( split )[ 2 .. 5 ] ), 1 }
   @array1;

print Data::Dumper->Dumpxs( [ \ %array1Lookup ], [ qw{ *array1Lookup }
+ ] );

open my $array2FH, q{<}, \ <<'EOF2' or die qq{open: < HEREDOC 2: $!\n}
+;
ATOM   2212  CB  MET L  52      17.332  94.112  87.029  1.00  0.00
ATOM   2213  CG  MET L  52      18.017  94.866  88.170  1.00  0.00
ATOM   2214  SD  MET L  52      18.711  96.457  87.699  1.00  0.00
ATOM   2215  CE  MET L  52      17.198  97.429  87.820  1.00  0.00
ATOM   2216  N   ARG L  53      19.331  91.671  87.132  1.00  0.00
ATOM   2217  CA  MET L  52      19.331  91.671  87.132  1.00  0.00
EOF2

my @array2 = ();
while ( <$array2FH> )
{
    chomp;
    my $lookupKey = join q{:}, ( split )[ 2 .. 5 ];
    next if $array1Lookup{ $lookupKey };
    push @array2, $_;
}
close $array2FH or die qq{close: < HEREDOC 2: $!\n};

print Data::Dumper->Dumpxs( [ \ @array2 ], [ qw{ *array2 } ] );
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The output.

%array1Lookup = (
                  'C:MET:L:52' => 1,
                  'N:MET:L:52' => 1,
                  'CA:MET:L:52' => 1,
                  'SG:CYS:L:51' => 1
                );
@array2 = (
            'ATOM   2212  CB  MET L  52      17.332  94.112  87.029  1
+.00  0.00',
            'ATOM   2213  CG  MET L  52      18.017  94.866  88.170  1
+.00  0.00',
            'ATOM   2214  SD  MET L  52      18.711  96.457  87.699  1
+.00  0.00',
            'ATOM   2215  CE  MET L  52      17.198  97.429  87.820  1
+.00  0.00',
            'ATOM   2216  N   ARG L  53      19.331  91.671  87.132  1
+.00  0.00'
          );
[download]

I hope I have guessed correctly and this is of some help.

Update: Added missing @ sigil to array2 in 2nd paragraph.

The problem for me is in regexp and intersection. To be very honest I have no idea how to use regexp for this particular task :( I am very new to perl so any guidance to material or example code will be really helpful

A few assumptions, "bold text" is the part of the text that is surrounded by [b] and [/b]. "bold text" isn't nested inside "bold text", and there's at most one piece of "bold text" per string. Strings not containing any bold text is to be ignored.

Then I would do something like (not tested):

my %seen;
m{\[b\](.*?)\[/b\]} and $seen{$1} = 1 for @array1;
my @result = grep {m{\[b\](.*?)\[/b\]} && !$seen{$1}} @array2;
[download]