We propose a model for a quintuple coupled quantum dot system based on a GaAs/AlGaAs heterostructure. Then, we analyze the optical bistability (OB) and optical multistability (OM) behaviours and transition between the regimes at a wavelength of λ μ = 1.550 m. We take the benefit of consecutive and parallel interdot tunnelling and an incoherent pumping field for electrical and even optical control of the processes. It is shown that OB, OM and transition between them can be accomplished and controlled by adjusting the rate of the inter-dot tunnellings (electrical bias), probe wavelength detuning and rate of the optical incoherent pumping field. By proper choice of the controlling parameters, the bistable hysteresis loop becomes narrower, which makes it easier for the cavity field to reach saturation. We interpret the OB and OM behaviours by discussing the absorption of the active medium. We also investigate switching time between the two stable states when the output field jumps from a lower branch to an upper branch. Such a controllable OB/OM and transition between them in multiple QD molecules at a wavelength of 1.550 μm, may provide some new possibilities for technological applications in optoelectronics, solid-state quantum information science and systems dealing with signal processing.