  This paper proves the following statement: If a convex body can form a
fivefold translative tiling in $\mathbb{E}^3$, it must be a parallelotope, a
hexagonal prism, a rhombic dodecahedron, an elongated dodecahedron, a truncated
octahedron, a cylinder over a particular octagon, or a cylinder over a
particular decagon, where the octagon and the decagon are fivefold translative
tiles in $\mathbb{E}^2$. Furthermore, it presents an example of multiple tiles
in $\mathbb{E}^3$ with multiplicity at most 10 which is neither a
parallelohedron nor a cylinder.
