In this talk, the results of student's research project concerning realizations of Lie algebras will be presented. Realizations of Lie algebras play an important role mainly in the theory of differential equations. By a realization, we mean a representation of the Lie algebra structure by vector fields. One of the natural problems is the classification of all realizations of a given Lie algebra. We will show how classification of so called transitive realizations corresponds to classification of subalgebras and how these transitive realizations can be easily explicitly computed by a method based on work of I. V. Shirokov et al. We use this method for construction of realizations of five-dimensional Lie algebras.