my @match;
while (<DATA>) {
  my $string_found = $_;
  push @match,( $string_found =~ /(first_string|second_string|third_st
+ring|fourth_string|fifth_string)/gm );
}
print scalar @match," matches found: ",join ", ",@match, "\n";
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Note that the var $string_found and the braces around the regex are superfluous