I think that the Green Pool of the Salinas River that bookends the story and the barn in Chapter 5 are two different settings that share equal importance. Both places are the backdrop in which there is a full realization of dreams dissipating. In both settings, characters are forced to confront the reality of dreams that have dwindled away, atrophying right before their very eyes. What once gave life and purpose is gone with both places- the barn and the green pool- serving as the backdrop. This makes both settings vital to the thematic development of Steinbeck's work.
The barn is where Lennie's dreams disappear forever. His initial dream of being able to tend to the puppies en route to tending to the rabbits is gone. The dead pup confirms this. Lennie knows this. He understands the full implications of what the dead animal means. This is enhanced with his realization that he has done something terrible when looking at Curley's wife's dead body. There is a full realization that his dream is over. Candy experiences the same reality when he curses at the corpse, recognizing that his own dreams and hopes have come to an end. The barn becomes the home to which dreams dying have been realized.
This is the same reality that dawns upon both Lennie and George in the Green pool of the Salinas River. This was the backdrop to the first chapter where the dreams of George and Lennie were first articulated. It is in this setting where they both settle at the end of the novel. As George tells Lennie about their dream, he shoots him. This confirms the death of their dreams. The setting here becomes home to the death of hope and aspirations. While both the barn and the green pool by the Salinas River are fundamentally different, they both operate in a similarly important thematic capacity.