I am wondering what is the best way to design the flow of my app in Android. There would be 5 main sections, so I was thinking in using 5 Tabs for this purpose. Inside every "section"/tab should be also some kind of navigation, so the user would navigate to new Activities, and here is were it comes a little bit tricky because I am not sure what would be the expected behaviour for the back button.
Applications such as Instagram have a similar structure and then when a user hits back he gets to the last Activity he was in, no matter if that is in a different Tab.
I think you can use Tab and Fragments. Its really nice to implements fragments if you want to navigate inside a Tab. You can see the doc for Fragment here. Here is the nice tutorial on TabActionBarSherlock.
And for back button you can use some flag for it. Update with the change and choose what to show to user when flag changes.
For start you can see this example on stackoverflow.Implementing action bar tabs with fragments.