In order to tackle the rapidly increasing traffic, the 5th generation (5G) mobile communication system will introduce small cells using higher frequency bands with wider bandwidth to achieve super high bit rate transmission of several tens of Gbps. Massive multiple input multiple output (MIMO) beamforming (BF) is promising as one of the technologies that can compensate for larger path-loss in the higher frequency bands. Joint analog fixed BF and digital precoding have been proposed to reduce the cost of a Massive MIMO transceiver. However, the conventional scheme assumes the transmission of a few streams using well-known codebook-based precoding as the digital precoding, and both a selection method of the fixed BF weights and a digital precoder design, which are suitable for super high bit rate transmission using multiple streams, have not been studied. This paper proposes a joint fixed BF and CSI-based precoding (called FBCP) scheme for the 5G Massive MIMO systems. FBCP first selects the analog fixed BF weights based on a maximum total received power criterion, and then it calculates an eigenmode (EM) precoding matrix by exploiting CSI. This paper targets a 5G system achieving over 20Gbps in the 20GHz band as one example. Throughput performances of the Massive MIMO using the proposed FBCP are evaluated by link level simulations using adaptive modulation and coding and it is shown that the proposed FBCP with the optimum number of selected beams (baseband chains) can use higher level modulation, up to 256QAM, and higher coding rates and achieve throughputs close to 30Gbps while the cost and complexity can be reduced compared with the fully digital Massive MIMO.