The accelerated expansion of the Universe and the rotational dynamics of Galaxies have become part of the mysteries of the physical world and have had theorists working tirelessly in the past years. There is no consensus on what is causing these observable effects: whether it is the yet-to-be-discovered dark energy and dark matter or it is the breaking down of our currently accepted theory of gravity, general relativity, on larger scales. In this paper, we assume it is the latter and analyse R n -gravity—a type of modified theory of gravity—in the Bianchi type-V spacetime. Numerous accelerating solutions are found and their stability is analysed. There is one particular solution that was found to be stable for a wide range of values of n and it makes for a possible solution for the accelerated expansion anomaly.