Help with Perl Script

I have a directory that has many different types of files but I need the script to zip on 3 files with differnent extensions.  For instance, the directory has  these file names:
12345.mar
12345.tst
12345.exn
12345.bbb
12345.xxx
but I only want to zip 12345.mar, 12345.tst, and 12345.xxx but with my script it is zipping all 5 files because I reference the client_id which is 12345.  The script is attached.
thanks,

# Create a zip file with the necessary files.
 
    my $client_zip_filename = File::Spec->catfile($product_dir,
   					        "product",
   					        sprintf("%s.zip",
                                          $client_id));
						
    # We want the files from the product directory that have the name <client>.*
 
        my $product_filename_regex = sprintf("^%s\\.", (length($client_id)<=5 ? $client_id."000":$client_id));
 
    opendir(ZIP_DIR, "$product_dir\\product") or die "cannot open: $!";
        my @files_to_zip = map {"$product_dir\\product\\$_"} grep {/$product_filename_regex/} readdir(ZIP_DIR);
    closedir(ZIP_DIR);
    $cmd = sprintf("\"c:\\program files\\7-zip\\7z\" a -tzip %s %s",
		   $client_zip_filename,
		   join(" ", @files_to_zip));
      if (system($cmd) != 0) {
	printf("Error executing command /%s/ with error = %d\n",
	       $cmd,
	       $CHILD_ERROR);
	next;
    }

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