What organ is on the left side about five inches below the breast at the edge of the rib cage?

There are a few... The stomach, colon, and spleen are probably the 3 closest organs to the area you are describing. The liver has a left lobe near here. Lastly, the small intestine can be found pretty close to this area, as well.
Spleen. The spleen is not normally (or barely) palpated in the left upper quadrant (luq) of the abdomen. It may be appreciable in thin people or if the spleen is enlarged.

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