In this study, we numerically evaluate the delay time characteristics of a two-step random access (RA) process proposed in the 5G standard. The 5G RA process comprises two RA stages, i.e., if the MsgA process fails a certain number of times in the two-step RA process, then it proceeds to the four-step RA process. Whereas the latency of the two-step RA is investigated more frequently compared with the four-step RA, the combination of two- and four-step RA operations has not been investigated. Therefore, in this study, we design a delay time analysis model by introducing the cumulative number of failures as an analysis parameter in a 5G two-step RA process. The 5G RA process uses 64 preambles to mitigate the RA collision probability. We evaluate the performance of the combined 5G RA process via two approaches, i.e., sharing 64 preambles and separating the preambles between two- and four-step RA processes. Results show that the preamble sharing method exhibits better delay time characteristics than the preamble separation method in the combined 5G RA process.