Nonrational Complete Intersections

The nonrationality of a general complete intersection $\bigcap_{i=1}^kF_i\subset{\mathbb P}^M$, where $F_i$ is a hypersurface of degree $d_i$, is proved under the condition that equality $\sum_{i=1}^kd_i=M$ holds and $\exists\,d_j\notin\{2,3,5\}$.