This paper proposes a novel quadrature space-frequency index modulation (QSF-IM) scheme as a promising energy-efficient radio-access technology for the fifth generation (5G) wireless systems. Motivated by the potential energy saving of spatial modulation (SM) with the part of information being carried through antenna indexes, the proposed scheme further leverages the benefits of SM by applying the idea across the spatial and frequency domains. Moreover, by deploying dual antenna constellation for in-phase and quadrature-phase transmission, the proposed scheme can enhance data rate at no extra cost of energy consumption, leading to further improvement in energy efficiency. Theoretical bit error rate and achievable sum-rate of the proposed scheme over frequency-selective correlated Rician and Rayleigh fading channels are derived and are shown to have good agreement with simulations. Furthermore, the effectiveness of the proposed scheme is analyzed through a comprehensive list of performance metrics, including spectral efficiency (SE), energy efficiency (EE), cost efficiency (CE), and economic efficiency. Performance trade-offs between these metrics are thoroughly investigated. Compared with other existing schemes, the proposed QSF-IM scheme is demonstrated to offer better EE-SE and EE-CE tradeoffs, and can therefore be considered as a potential candidate for energy-spectral efficient 5G systems.