Solving the power flow (PF) equations based on Newton–Raphson technique has been considered in the literatures since the late 1960s. Ever since, various types of studies have been presented about the solution of the PF problem. The main purpose of the presented methods is to decrease the computation time. This study presents applying the third-, fourth- and fifth-order Newton-like methods to solve the PF problem in power systems. Using the third-, fourth- and fifth-order methods in solving the PF problem can significantly reduce the computation time and the number of iterations. The proposed formulations and algorithms are tested on standard 9-, 14-, 30-, 57-, 118- and 2383-bus systems and the results are reported and discussed.