5. In the cube $A B C D-A_{1} B_{1} C_{1} D_{1}$, $E$ is the midpoint of $B C$, and $F$ is on $A A_{1}$ such that $A_{1} F: F A=1: 2$. Find the dihedral angle formed by the plane $B_{1} E F$ and the base $A_{1} B_{1} C_{1} D_{1}$.
(1985 National High School League Problem)
5. $\arccos \frac{3 \sqrt{46}}{46}$.