The unstable nucleus 5 He emission has never been included in the widely used statistical model codes as the evaluation tool and interpretation experimental data. The calculated threshold energies of 5 He emission from light nuclei to heavy nuclei indicate that in most cases the compound nucleus induced by incident neutron would emit 5 He rather than 3 He. Since 5 He is unstable and can be separated into n+α spontaneously, so neutron is produced in 5 He emission process. The formulation of the double-differential cross section of the neutron from the two-body breakup process of emitted 5 He is established. Because of the strong recoil effect, the energy balance is strictly taken into account to meet the needs in nuclear engineering. Further improvement of the statistical model calculation codes on this respect is proposed. It is expected that the correlative measurement will be available to account the outgoing neutron and alpha particle simultaneously and to test and verify the existence of 5 He emission.