This paper presents a partially parallel low-density parity-check (LDPC) decoder designed for the 5G New Radio (NR) standard. The design is using a multi-block parallel architecture with a flooding schedule. The decoder can support any code rates and code lengths up to the lifting size Zmax= 96. To compensate for the dropped throughput associated with the smaller Z values, the design can double and quadruple its parallelism when lifting sizes Z<= 48 and Z<= 24 are selected respectively. Therefore, the decoder can process up to eight frames and restore the throughput to the maximum. To simplify the design's architecture, a new variable node for decoding the extended parity bits present in the lower code rates is proposed. The FPGA implementation of the decoder results in a throughput of 2.1 Gbps decoding the 11/12 code rate. Additionally, the synthesized decoder using the 28 nm TSMC technology, achieves a maximum clock frequency of 526 MHz and a throughput of 13.46 Gbps. The core decoder occupies 1.03 mm2, and the power consumption is 229 mW.