  We construct all possible complete intersection Calabi-Yau five-folds in a
product of four or less complex projective spaces, with up to four constraints.
We obtain $27068$ spaces, which are not related by permutations of rows and
columns of the configuration matrix, and determine the Euler number for all of
them. Excluding the $3909$ product manifolds among those, we calculate the
cohomological data for $12433$ cases, i.e. $53.7 \%$ of the non-product spaces,
obtaining $2375$ different Hodge diamonds. The dataset containing all the above
information is available at
https://www.dropbox.com/scl/fo/z7ii5idt6qxu36e0b8azq/h?rlkey=0qfhx3tykytduobpld510gsfy&dl=0
. The distributions of the invariants are presented, and a comparison with the
lower-dimensional analogues is discussed. Supervised machine learning is
performed on the cohomological data, via classifier and regressor (both fully
connected and convolutional) neural networks. We find that $h^{1,1}$ can be
learnt very efficiently, with very high $R^2$ score and an accuracy of $96\%$,
i.e. $96 \%$ of the predictions exactly match the correct values. For
$h^{1,4},h^{2,3}, \eta$, we also find very high $R^2$ scores, but the accuracy
is lower, due to the large ranges of possible values.
