The main goals of fifth generation (5G) systems are to significantly increase the network capacity and to support new 5G service requirements. Ultra network densification with small cells is among the key pillars for 5G evolution. The inter-small-cell 5G backhaul network involves massive data traffic. Hence, it is important to have a centralized, efficient multi-hop routing protocol for backhaul networks to manage and speed up the routing decisions among small cells, while considering the 5G service requirements. This paper proposes a parallel multi-hop routing protocol to speed up routing decisions in 5G backhaul networks. To this end, we study the efficiency of utilizing the parallel platforms of cloud computing and high-performance computing (HPC) to manage and speed up the parallel routing protocol for different communication network sizes and set recommendations for utilizing cloud resources to adopt the parallel protocol. Our numerical results indicate that the HPC parallel implementation outperforms the cloud computing implementation, in terms of routing decision speed-up and scalability to large network sizes. In particular, for a large network size with 2048 nodes, our HPC implementation achieves a routing speed-up of 37x. However, the best routing speed-up achieved using our cloud computing implementation is 15.5x, and is recorded using one virtual machine (VM) for a network size of 1024 nodes. In summary, there is a trade-off between a better performance for HPC vs. flexible resources of cloud computing. Thus, choosing best fit platform for 5G routing protocols depends on the deployment scenarios at 5G core or edge network.INDEX TERMS 5G routing protocol, Cloud Radio Access Networks, Cloud computing, HPC, Ultra-Dense Network.