  We perform a Noether analysis for a description of translation
transformations in 4D $\kappa$-Minkowski noncommutative spacetime which is
based on the structure of a 5D differential calculus. The techniques that some
of us had previously developed (hep-th/0607221) for a description of
translation transformations based on a 4D differential calculus turn out to be
applicable without any modification, and they allow us to show that the basis
usually adopted for the 5D calculus does not take into account certain aspects
of the structure of time translations in $\kappa$-Minkowski. We propose a
change of basis for the 5D calculus which leads to a more intuitive description
of time translations.
