Velaki,
In your description, you say the date is in the format MM/DD/YY, but in your code it looks like it is a 4 digit year. Out of idle curiosity, does the following run any faster?

#!/usr/bin/perl
use warnings;
use strict;

my $file = $ARGV[0] || 'bigfile.dat';
open (INPUT, '<', $file) or die "Unable to open $file for reading : $!
+";

my %date;
my $pos = tell INPUT;

while ( <INPUT> ) {
    my @field = split /\|/;
    push @{ $date{ join '', (split m|/|, $field[4])[2,0,1] } }, $pos;
    $pos = tell INPUT;
}

for ( sort { $a <=> $b } keys %date ) {
    for ( @{ $date{ $_ } } ) {
        seek INPUT, $_, 0;
        print scalar <INPUT>;
    }
}
[download]

I am also a little curious if they generate the same output. My version should preserve the order when two or more dates are the same. For anyone interested in micro-optimization, unpack 'x6A4X10A2xA2', $field[4] might be faster than the split/slice combo but is untested.