After a little playing around, I came up with this:

#!/usr/bin/perl -w 

use strict;

my @stuff = qw(1234 a12345 12345 12345z 123456);

foreach my $num (@stuff) {
    unless ($num =~ /^\d{5,}$/) {
        print "Not Valid: $num\n";
    } else {
        print "Valid: $num\n";
    }
}
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Note the $ anchor there...this should match any string of digits that's at least 5 digits long, and it will fail for anything with non-digits in it.

EDIT: Removed the extra crap before the $ anchor.