It seems like you're interested in the edit distance. There are several different algorithms, and the most well-known is Levenshtein distance, implemented for example by Text::Levenshtein.

#!/usr/bin/perl
use warnings;
use strict;

use Text::Levenshtein qw{ distance };

use Test::More tests => 3;

is distance('ABCGE', 'ABCGE'), 0;
is distance('ABCGE', 'FGCGB'), 3;
is distance('ABCGE', 'JHAGT'), 4;
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