This paper details an experimental testbed conceived for studying the capability of new multicarrier waveforms to accommodate 5G requirements. Testbed experiments are done with an implementation of cyclically prefixed orthogonal frequency division multiplexing (CP-OFDM) and its most promising enhancements, i.e., weighted overlap and add based OFDM (WOLA-OFDM) and block-filtered OFDM (BF-OFDM), with configurable universal software radio peripherals (USRPs) based software defined radio (SDR) prototype. These experiments are done in a realistic laboratory-like environment where capabilities of the selected waveforms to accommodate 5G requirements are evaluated while focusing on the optimization of the energy efficiency. On one hand, we provide details and deign guidance to improve energy efficiency and robustness of the studied waveforms through new approaches of digital predistortion (DPD) and peak-to-average power ratio (PAPR) reduction in presence of RF power amplifier (RF PA). In particular, we focus on the mitigation of in-band and out-of-band non-linear distortions and their effects on power spectrum density (PSD) and bit error rate (BER), respectively. It has been demonstrated that the combination of PAPR reduction and DPD allows the transmitter to significantly improve the spectrum localization without sacrificing the in-band and out-of-band waveform quality, while achieving high power efficiency, thus operating the PA very close to its saturation region, as well. On another hand, we address the impact of the lack of synchronism between transmitters on the performance of the selected waveforms, which is of special relevance for future 5G massive machine type communications (mMTC) applications. Experimental results show that BF-OFDM and WOLA-OFDM would permit the accommodation of 5G requirements when RF PA issues are tackled. In some specific scenarios, ideal spectrum utilization can be realized by these waveforms, using only one tone as guard band while keeping good energy efficiency.