We study five-point correlation functions of scalar operators in $\textit{d}$-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 〈$\textit{σσϵσσ}$〉 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 ∆ ⩽ ∆ . We then compute several OPE coefficients involving $\textit{ϵ}$ and two spinning operators by demanding that the truncated correlator approximately satisfies the crossing relation.