"Sliding window" is a decptive title, but the problem is interesting.

A not very perlish solution:

#! perl -slw
use strict;

my %hash = (a=>2, b=>1, c=>5, d=>3, e=>4);

my $input = "abcdaeec";
our $N //= 2;

$,= ' ';
print map{
    my $iplus = ord() - ord('a');
    $iplus = ( $iplus + $N ) % keys %hash;
    $iplus = chr( ord('a') + $iplus );

    $hash{ $_ } + $hash{ $iplus };
} split '', $input;

__END__
C:\test>junk41 -N=2
7 4 9 5 7 5 5 9

C:\test>junk41 -N=3
5 5 7 4 5 9 9 7

C:\test>junk41 -N=4
6 3 6 8 6 7 7 6
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