There are a couple of issues, here. The first is that you always want to use

use warnings;
use strict;
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Next, you're using a scalar as the argument to your 'sort' routine. 'sort' is going to want an array and it'll return the sorted array.

Next, you should consider using Date::Simple or (for more complex stuff) DateTime. To do this, you first install the module, then something like:

use DateTime;

my @dates;
while(<...>)
{
  my $date = DateTime->new(...);
  push @dates, $date;
}

my @sorted = sort @dates;
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Hope that helps!

Update: fixed a typo