#!/usr/bin/perl
use strict;
use warnings;

while (<DATA>) {
my $string_found = $_;
my @match = ( $string_found =~ /(first_string|second_string|third_string|fourth_string|fifth_string)/gm );
print scalar @match," matches found: ",join ", ",@match, "\n";
}

__DATA__
This is a test file matchme ljldjlfjd l;djfldjlf d
test test test dljfldjlfjldjfldjlljdf one second_string
dlfjldfj  ljdfldjjf ldjfljdl dfljdlfj dfdlfj
three ljfldjlj dlfjlasdj foiidufoiida matchdf
dljfldsaofuoidfousdaof ladsjflasdof first_string
dlfjodsuofuasdo sadoufosadu foasduf aosduf third_string

__Current results__
0 matches found: 
1 matches found: second_string, 
0 matches found: 
0 matches found: 
1 matches found: first_string, 
1 matches found: third_string,

__Wanted results__
3 matches found: second_string, first_string, third_string