Normal projective varieties of degree 5

We list the irreducible reduced and not degenerate normal projective varieties $X\subset {\mathbb{P}}^N$ of dimension $n$ and degree five defined over an algebraically closed field $k$ of char$(k)=0$. In the smooth case, or when $n=2$, we give also classification results for any algebraically closed field $k$ of char$(k)\ge 0$.