I am studying Multizeta values at the moment and I found that at weight 5, the basis is given by $\zeta(5)$ and $\zeta(3)\zeta(2)$ in the literature. Solving all shuffle and stuffle relations using mathematica I, however, get as a basis $\zeta(5)$ and $\zeta(4,1)$.
Are there any further relations which relate $\zeta(3)\zeta(2)$ and $\zeta(4,1)$ so that they are secretely the same thing?