  We give an upper bound for the least energy of a sign-changing solution to
the the nonlinear scalar field equation $$-\Delta u = f(u), \qquad u\in
D^{1,2}(\mathbb{R}^{N}),$$ where $N\geq5$ and the nonlinearity $f$ is
subcritical at infinity and supercritical near the origin. More precisely, we
establish the existence of a nonradial sign-changing solution whose energy is
smaller that $12c_0$ if $N=5,6$ and smaller than $10c_0$ if $N\geq 7$, where
$c_0$ is the ground state energy.
