Consider extracting all the things that look like a year number, and changing the matching logic to first check for the equivalence of the years and then falling back on the five words equivalence. Something like:

my $year_left = ...;
my $year_right = ...;

my $have_years = ($year_left and $year_right);
my $equal_years = ($year_left == $year_right);

my $five_words_result = ...; # you already have this above

my $final_result;

if( ! $have_years ) {
    $final_result = $five_words_result;
} elsif( $equal_years ) {
    $final_result = $five_words_result;
} elsif( ! $equal_years ) {
    $final_result = undef; # without matching years, things are never 
+equal
} else {
    die "This should never happen. left=$year_left, right=$year_right,
+ have_years=$have_years, equal_years=$equal_years";
};
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Maybe it would be good to put this logic, together with the logic for finding five or more matching words, into its own function. Consider passing to that function the title on the left side and the title on the right side, and possibly already the extracted year numbers.