Thanks very much for all your comments so far. With that in mind, I changed some of my code as follows

foreach my $key (sort keys %csa_hash)
{
    #print "$key\n";
    
    # ok we now need to split up the key in the hash
    
    my $pdb = substr($key, 0, 4);
    
    my $chain = substr($key, 5, 1);
    
    my $res = substr($key, 7, 6);
        
    #print "$pdb $chain $res\n"; # works great. using substring as I d
+ont really want to create an array
    
    my $pdbchain = "$pdb" . "$chain"; # concatenate together so to com
+pare with domain data
    
    # print "$pdbchain\n"; # works fine
    
    # lets be on the safe side and remove white space
    # for domchain and pdbchain
    
    $res =~ s/\s//g;
    #$domchain =~ s/\s//g;
    $pdbchain =~ s/\s//g;
    
    #chomp($domchain);
    chomp($pdbchain);
    
    if($dom_hash{$pdbchain}{$res})
    {
    print "$pdbchain $res\n";
    }   
}
[download]

And now it runs in seconds. I'm no longer looping over %dom_hash, I'm simply using it as a look up table.