  One of the main aims of phylogenetics is to reconstruct the \enquote{Tree of
Life}. In this respect, different methods and criteria are used to analyze DNA
sequences of different species and to compare them in order to derive the
evolutionary relationships of these species. Maximum Parsimony is one such
criterion for tree reconstruction and, it is the one which we will use in this
paper. However, it is well-known that tree reconstruction methods can lead to
wrong relationship estimates. One typical problem of Maximum Parsimony is long
branch attraction, which can lead to statistical inconsistency. In this work,
we will consider a blockwise approach to alignment analysis, namely so-called
$k$-tuple analyses. For four taxa it has already been shown that
$k$-tuple-based analyses are statistically inconsistent if and only if the
standard character-based (site-based) analyses are statistically inconsistent.
So, in the four-taxon case, going from individual sites to $k$-tuples does not
lead to any improvement. However, real biological analyses often consider more
than only four taxa. Therefore, we analyze the case of five taxa for $2$- and
$3$-tuple-site data and consider alphabets with two and four elements. We show
that the equivalence of single-site data and $k$-tuple-site data then no longer
holds. Even so, we can show that Maximum Parsimony is statistically
inconsistent for $k$-tuple site data and five taxa.
