use strict;
use warnings;

my $matchCount = 0;
while( <DATA> )
{
    $matchCount += () = m{(
       first_string
       |
       second_string
       |
       third_string
       |
       fourth_string
       |
       fifth_string)}xg;
}
print qq{$matchCount matches found\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