  We obtain improved Fourier restriction estimate for the truncated cone using
the method of polynomial partitioning in dimension $n\geq 3$, which in
particular solves the cone restriction conjecture for $n=5$, and recovers the
sharp range for $3\leq n\leq 4$. The main ingredient of the proof is a
$k$-broad estimate for the cone extension operator, which is a weak version of
the $k$-linear cone restriction estimate for $2\leq k\leq n$.
