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In this paper, we have introduced a novel five-dimensional (5D) hyperchaotic system by extending the well-known Lorenz system. The dynamical properties of the system are analysed by calculating the Lyapunov exponents, graphing the phase portraits, bifurcation diagrams, the time series and by finding the Kaplan–Yorke dimension. The equilibrium points of the system have been calculated and the stability analysis of these equilibrium points is discussed. Hybrid function projective synchronisation has been carried out between the identical systems using the scheme of adaptive control. Suitable controllers have been designed to attain the desired synchronisation between the systems using Lyapunov stability theory. The theoretical results have been validated by performing numerical simulations using the MATLAB. [ABSTRACT FROM AUTHOR]