Wireless communications and electromagnetic applications make use of a sensor array which is made up of antenna elements. Direction of arrival (DOA) estimation refers to the process of determining at a receiving antenna array, the angles from which the different source signals impinge the array. Root MUSIC and Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT) are two such algorithms which do not use the spatial spectrum to estimate the DOAs. Root MUSIC finds the roots of a polynomial which correspond to the DOAs and ESPRIT makes use of sub-arrays (named as doublets) within the main array to find the DOAs. In this paper, we have simulated these two algorithms at a 5G frequency of 30 GHz (wavelength is 0.01 m) considering a uniform linear array (ULA) of 72 elements. Twelve (12) sources were considered for DOA estimation. At the millimeter wave (mmWave) frequencies, it is possible to have dense arrays which can accommodate a large number of antenna elements within a small space. We have evaluated the Root mean square error (RMSE) for the two algorithms by varying the number of snapshots, inter-element spacing and number of elements; respectively. It is seen that the Root MUSIC algorithm outperformed the ESPRIT under good radio channel conditions.