Far away from the hard theory of representations, we study the noncommutative Fourier analysis on the (2, 3, 5) group (called the Cartan group 5 G , or the generalized Dido problem), which can be shown to be a semi-direct product of three real vector groups. This led to the construction of a larger group to introduce the Fourier transform and obtain the Plancherel formula on . 5 G We denote the complexified universal enveloping algebra of the real Lie algebra of 5 G by , U and prove that U is globally solvable. Further, we obtain the classification of all right ideals in the group algebra of . 5 G Finally, by Hormander theory, we solve the division problem of distributions on this group.