We provide a local as well as a semi-local analysis of a fifth convergence order scheme involving operators valued on Banach space for solving nonlinear equations. The convergence domain is extended resulting a finer convergence analysis for both types. This is achieved by locating a smaller domain included in the older domain leading this way to tighter Lipschitz type functions. These extensions are obtained without additional hypotheses. Numerical examples are used to test the convergence criteria and also to show the superiority for our results over earlier ones. Our idea can be utilized to extend other schemes using inverses in a similar way.