This paper proposes a carrier-less amplitude and phase modulation passive optical networks (CAP-PON) scheme based on dynamic probabilistic shaping (DPS) and Rubik's cube encryption in optical access networks. The key is generated from a novel five-dimensional entangled chaos model for dynamic probabilistic shaping and Rubik’s cube encryption. To verify the performance of the encryption scheme, an experimental demonstration of 70 Gb/s (7×10Gb/s) encrypted DPS-3D-CAP signal transmission over 2 km weakly coupled 7-core fiber is performed. The key space of the new five-dimensional entangled chaos model reaches 10¹⁷³ the interference level reaches 100%. Experimental results show that the receiver sensitivity increases by 1.47 dB compared to the conventional uniform 3D-CAP due to the introduction of dynamic probabilistic shaping.