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In the massive Machine Type Communications (mMTC) scenario of the 5G network, a huge number of devices communicate with each other. The massive access requests will cause frequent access collisions, which will reduce the efficiency of Random Access (RA) procedure. In this paper, we propose the random power back-off scheme that utilizes power domain Non-orthogonal Multiple Access (NOMA) scheme to solve the RA collision problem in 5G networks. In the proposed method, we attempt to mitigate the RA conflict situation when devices send the same preamble even if the Base Station (BS) does not detect the preamble collision. The proposed method is shown to improve the RA efficiency and average delay.