There are many ways to do it but here is a pretty simple and self explanatory one:

use strict;
use warnings;
use Date::Calc qw(check_date);

my $date = "9999/12/11";
my($year,$month,$day) = $date =~ /(\d+)\/(\d+)\/(\d+)/;
print "$year/$month/$day is ";
if(check_date($year,$month,$day) && $year >=1753 && $year <= 9999)
{
    print "valid";
}
else
{
    print "not valid\n";
}
[download]

I don't think you are going to be able to do a complete validation using just a regex.

Chris