boo_radley's solution is intriguing:

unless ($num =~ /^\d{5,}/ && $num !~/\w/)

According to Robert's Perl Tutorial "The \w construct actually means 'word' - equivalent to a-zA-Z_0-9"

Because \w includes digits it looks as if this regex might reject all numbers. I tried out the following code here:

my $num = "123456";
unless ($num =~ /^\d{5,}/ && $num !~/\w/) {
    print p("Sorry, $num does not match the regex");
} else 
    {print p("$num matched")};
[download]

and sure enough the number 123456 did not match the regex.