$domchain =~/\S/g;
        $pdbchain =~/\S/g; 

        chomp($domchain);
        chomp($pdbchain);
[download]

I tried to fix some things in the code below, but, naturally, I could't try to run it (as I don't have the files).

use strict;
use warnings FATAL => 'all';
use autodie;

my $dir = "<my directory>";
my ( $dom_file_name, $csa_file_name ) = @ARGV;
my %csa_hash;
my %dom_hash;

open my $csa_file, '<', $csa_file_name;
while ( my $csa = <$csa_file> ) {
    my @csa_data = split( /\,/, $csa );
    $csa_hash{ $csa_data[0] . $csa_data[3] } = $csa_data[4];
}
close($csa_file);

open my $dom_file, '<', $dom_file_name;
while ( my $dom = <$dom_file> ) {
    my @dom_data = split /\s+/, $dom;
    my $domain = $dom_data[0];
    next if exists $dom_hash{$domain};
    open my $ind_dom_file, '<', $dir . $domain;
    while ( my $line = <$ind_dom_file> ) {
        chomp $line;
        my @ff     = split /\s+/, $line;
        my $number = $ff[5];
        my $CA     = $ff[2];
        push @{ $dom_hash{$domain} }, $number if $CA eq 'CA';
    }
    close $ind_dom_file;
}
close $dom_file;

while ( my ( $protein_dom, $residues_ref ) = each %dom_hash ) {
    for my $residue ( @{$residues_ref} ) {
        my $dom_chain = substr( $protein_dom, 0, 5 );
        if ( $residue eq $csa_hash{$dom_chain} ) {
            print "$dom_chain $residue\n";
        }
    }
}
[download]

The idea was that it does the same thing as your code, but faster.