No-core Gamow shell model (NCGSM) is applied to study selected well-bound and unbound states of helium isotopes. This model is formulated on the complex energy plane and, by using a complete Berggren ensemble, treats bound, resonant, and scattering states on equal footing. We use the density matrix renormalization group method to solve the many-body Schrodinger equation. To test the validity of our approach, we benchmarked the NCGSM results against Faddeev and Faddeev-Yakubovsky exact calculations for H-3 and He-4 nuclei. We also performed ab initio NCGSM calculations for the unstable nucleus He-5 and determined the ground-state energy and decay width, starting from a realistic (NLO)-L-3 chiral interaction