Which method are you talking about, with respect to those 5 seconds?  The XOR method outlined above takes just ~0.05 secs on my 4-year-oldish machine, for 10,000 comparisons against a common 40-char target (with ~3-5 deviations per sequence):

my @set = qw(A T C G);
my $target = join "", map $set[rand @set], 1..40;
my @tests ;
for (1..10000) {
    my $test = $target;
    for (1..5) {
        substr($test, rand(length($target)), 1) = $set[rand @set];
    }
    push @tests, $test;
}


use Time::HiRes qw(time);
my $start = time();

my %change;  # reverse lookup table
for my $t1 (@set) {
    my $t = $t1;
    $t =~ tr/ATCG/HRDZ/;
    for my $t2 (@set) {
        $change{ $t ^ $t2 } = "$t1->$t2";
    }
}

$target =~ tr/ATCG/HRDZ/;

for my $test (@tests) {
    my $diff = $target ^ $test;
    while ($diff =~ /([^\x09\x06\x07\x1d])/g) {
        my $pos    = pos($diff);
        my $change = $change{$1};
        # do something with them...
    }
}

printf "%.3f secs\n", time() - $start;

__END__
0.052 secs
[download]

Storing away the results somewhere or doing something else with them will presumably take considerably longer than computing them...