It is anticipated that much higher network capacity will be achieved by the fifth generation (5G) small cell networks incorporated with the millimeter wave (mmWave) technology. However, mmWave signals are more sensitive to blockages than signals in lower frequency bands, which highlights the effect of anisotropic path loss in network coverage. According to the fractal characteristics of cellular coverage, a multi-directional path loss model is proposed for 5G small cell networks, where different directions are subject to different path loss exponents. Furthermore, the coverage probability, association probability, and the handoff probability are derived for 5G fractal small cell networks based on the proposed multi-directional path loss model. Numerical results indicate that the coverage probability with the multi-directional path loss model is less than that with the isotropic path loss model, and the association probability with long link distance, e.g., 150m, increases obviously with the increase of the effect of anisotropic path loss in 5G fractal small cell networks. Moreover, it is observed that the anisotropic propagation environment is having a profound impact on the handoff performance. Meanwhile, we could conclude that the resulting heavy handoff overhead is emerging as a new challenge for 5G fractal small cell networks.