If you want to go more into detail you can cut the bulged part out and connect it with a loft to get the connecting curvature perfect and trim it off or just connect it with a complete loft.
@SCALEMODEL - I am trying to duplicate what you have done here, but I am not sure how to draw the guide lines in 3D space between the Revolved body and the added pentagon sketch.
Making guides is little bit tricky, I use 3 Points Construction Plane, but first I align with Construction Axis and move it to create 3 snapping points.