•The study of new unknown details in nitrogen spectroscopy is an important part of chemistry background.•A new spin-forbidden quintet-triplet C’’5Πu → B3Πg transition is predicted.•Transition probabilities for an unknown C’’5Пu → B3Пg system of vibronic bands are calculated.•We provide SOC constants calculated by MRCI calculations which are in a good agreement with experiment.•The experimental set-up designed to detect the C’’ → b transition can also be used to observe the A′→ a emission. A new spin-forbidden quintet-triplet C′′5Πu → B3Πg transition is predicted in the N2 molecule on the ground of MRCI calculations with account of spin-obit coupling (SOC) by perturbation theory. The mechanism of its probability borrowing is quite similar to the recently calculated spin-forbidden electric dipole A′5Σg+ → A3Σu+ transition in the emission spectrum of the N2 molecule. Neither of the two predicted emission systems have yet been observed in electric discharges but the calculated intensity provides a good chance for their detection. Both transitions, C′′–B and A′–A, borrow intensity from the First Positive System (B3Πg → A3Σu+) and from the Herman Infrared Band (C′′5Πu → A′5Σg+). The latter spin-allowed quintet-quintet transition provides strong depletion of the upper C′′ state; nevertheless, the energy pooling collisions of the triplet N2 molecule and atomic recombination produce a permanent pumping of the C′′5Πu states leaving a prominent emission with a detectable quantum yield. The proposed C′′ → B vibronic transitions have Einstein A coefficients in the order of 105–104s −1, showing a considerable number of strong vibronic bands. As a consequence, the radiative lifetimes of the highest spin sublevel of the C′′5Πu,1 irregular state are about 10−6 s.