With 5 players, we're able to win with 7 epidemics + Virulent/Mutation about half the time. In the last game we played, we were short one action and therefore lost by decking ourselves (lame!). Note that having 5 players isn't really an advantage -- it mainly just makes you more likely to deck yourself before you get 4 cures.
We tend to do better if we draw a good balance between role types, where we have at least one of the three major categories: movement/coordination (e.g. Operation's Expert and Dispatcher), treatment (e.g. Medic and Containment Specialist), and cure-finding (e.g. Scientist and Researcher).
Most of all, though, you need a role in the movement/coordination category -- it's just so expensive to get around the board normally.
I don't like to recommend variations I haven't tried, but you can probably reach 7 more easily if you give yourself more choice in starting roles. For example, during setup you could allow each player one chance to discard her role and draw again.