Interesting. I would agree 5 miles is not far enough. It's good enough to get you started cycling and building some biking fever, but without seeing a map of your potential routes, it may be better to ride a different route at different times.
It might be difficult to live long and prosper if you're dizzy on a bike with fast traffic and weak muscles. I used to avoid above 35mph roads, but now if road has wide shoulders and no obstructions, I will ride on 45 mph roads.
I don't know about riding in neighborhood, it might be hard to find longer stretches where you can build speed. How about going to a bike shop and seeing if there are any local rides, and then finding out where they ride.