Is there a better solution than this?

It depends, are the values in the set unique if converted to upper case and are the numbers always less than say 10 digits ?

Update - assuming answers are yes try

#!perl
use strict;
my %out=();
while (<DATA>){
  chomp;
  my $key = uc $_;
  $key =~ s/(\d+)/sprintf("%010d",$1)/eg;
  $out{$key} = $_;
}

print "$out{$_} ($_)\n" for (sort keys %out);

__DATA__
blank_5_str_1
blank_5_str_10
blank_5_str_11
blank_5_str_12
blank_5_str_13
blank_5_str_14
blank_5_str_2
blank_5_str_3
blank_5_str_4
blank_5_str_5
blank_5_str_6
blank_5_str_7
blank_5_str_8
blank_5_str_9
[download]

poj