Using different modules, Time::Local and POSIX, is a direct way to compute today's date in UTC to compare to the dates in the file which are UTC. That avoids all the function calls in the loop you built, which really slow down the program.

#!/usr/bin/perl
use strict;
use warnings;
use Time::Local qw/ timegm_nocheck /;
use POSIX qw/ strftime /;

my $n = 4;
my ($d, $m, $y) = (gmtime)[3..5];
my $gmtime = strftime "%d/%b/%Y", gmtime timegm_nocheck 0,0,0, $d-$n, 
+$m, $y;
$gmtime =~ s/^(?:0| )//;

while(<DATA>){
    print if /$gmtime\b/;
}
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But to impliment some of the time saving 'tricks' suggested by others in this thread would involve a while loop with more code.