In this piece of research, our aim is to investigate the novel solitons solutions of nonlinear (4+1)-dimensional Fokas equation (FE) and (2+1)-dimensional Breaking soliton equation (BSE) via new extended direct algebraic method. New acquired solutions are bright, singular, dark, periodic singular, combined-dark bright and combined-dark singular solitons solutions along with hyperbolic and trigonometric functions solutions. The achieved distinct types of solitons solutions contain key applications in engineering and physics. By taking the appropriate values of involved parameters, numerous novel structures are also plotted. These solutions define the wave performance of the governing models, actually.