The conventional detectors that require high computational complexity can not be applied in complicated 5G systems, where many new techniques (massive MIMO and mmWave) to be employed. This paper proposes a new detector for 5G systems, called tensor decomposition deep learning (3-D DL). We show that the 5G systems can be expressed as a deep learning network in an equivalent tensor form, where the affine transformation is replaced by the multi-linear and multi-way. Such multi-way information then is preserved through layer wise factorization, where the tensor decomposition and nonlinear activation are performed in each hidden layer. Finally, the tensor-decomposed error backpropagation is developed to train the established network. This 3-D DL fully exploits the advantages of the multi-dimensional structural information of signals, to accomplish the estimations with higher resolution. It also avoids the disregard of structural information across different ways and high complexity found in the traditional methods