  We study five-point correlation functions of scalar operators in
d-dimensional conformal field theories. We develop a new approach to computing
the five-point conformal blocks for exchanged primary operators of arbitrary
spin by introducing a generalization of radial coordinates, using an
appropriate ansatz, and perturbatively solving two quadratic Casimir
differential equations. We then study five-point correlators $\langle \sigma
\sigma \epsilon \sigma \sigma \rangle$ in the critical 3d Ising model. We
truncate the operator product expansions (OPEs) in the correlator by including
a finite number of primary operators with conformal dimension below a cutoff
$\Delta \leqslant \Delta_{\rm cutoff}$. We then compute several OPE
coefficients involving $\epsilon$ and two spinning operators by demanding that
the truncated correlator approximately satisfies the crossing relation.
