We present new exact solutions in the form of solitary waves for the conformableKlein-Gordon equation with quintic nonlinearity. We use functional variable method which convertsa conformable PDE to a second-order ordinary differential equation through a traveling wavetransformation. We obtain periodic wave and solitary wave solutions including particularly kink-profile and bell-profile type solutions. The present method is a direct and concise technique whichhas the potential to be applicable to many other conformable PDEs arising in physics and engineering
