<p>In this article, we have designed a fifth-order conformable iterative method to solve nonlinear and transcendental equations. The proposed method exhibits superior stability, efficiency, computational performance, and convergence speed compared to the existing Newton and Traub methods. This is demonstrated through mathematical models such as the Shockley diode equation, biometric human arm motion, and signal processing models. Furthermore, we have generalized our proposed method to solve systems of nonlinear equations and conducted a detailed convergence analysis. Numerical experiments have been performed, and the Approximated computational order of convergence (<i>ACOC</i>) validates the theoretical findings. Additionally, in some numerical experiments, it is observed that conformable iterative methods outperform classical iterative methods. Moreover, the stability of the proposed method is illustrated using convergence plane analysis.</p>