Here are two untested solutions to give you a starting point.

This first one uses DateTime.

#!/usr/bin/perl
use DateTime;
use DateTime::Format::Flexible;

my $date = 'Wednesday, May 20, 2009 2:09 PM';
my $dt = DateTime::Format::Flexible->parse_date_time( $date );
print 'The day of year is ', $dt->day_of_year(), "\n";
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The second uses Date::Calc.

#!/usr/bin/perl
use Date::Calc qw( Day_of_Year );
print 'The day of year is ', Day_of_Year(2009, 5, 20), "\n";
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