#!/usr/bin/perl -w
use strict;

my $infile = 'some_logfile';
my $outfile = 'new_logfile';
my $datematch = qr(2005-5-3); # or whatever

open IN, "<", $infile or die "Cannot open $infile:$!\n";
open OUT, ">", $outfile or die "Cannot open $outfile:$!\n";

while (<IN>) {
    next if !/$datematch/;
    print OUT $_;
}

close IN;
close OUT;