it doesn't recognise regular Real numbers like -2, -5

It does, here's a way you can test that (see e.g. How to ask better questions using Test::More and sample data):

use warnings;
use strict;
use Test::More;
use Regexp::Common qw/number/;

like  "-2", qr/^$RE{num}{real}$/;
like  "-5", qr/^$RE{num}{real}$/;
like " -5", qr/^$RE{num}{real}$/;

done_testing;

__END__

ok 1
ok 2
not ok 3
#   Failed test at ...
1..3
# Looks like you failed 1 test of 3.
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As you can see, the problem isn't that it doesn't match integers, it's the whitespace at the beginning of the line. Try changing

    next if /^($RE{num}{real})/ && $1 > $limit;
    next if /^(\s\s-\d)/ && $1 > $limit;
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to

    next if /^\s*($RE{num}{real})/ && $1 > $limit;
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Where \s* means "zero or more whitespace characters" (perlretut).