I’ve had a chance to read through the Beginner Box Transitions document, for converting your Pathfinder BB game to a Pathfinder Core game. As I mentioned earlier, it is not really a document for continuing your BB game beyond 5th level. However, a clever GM could use the document to continue on to 6th level, at least for the four classes included in the BB (refer to pages 17-21, just ignore the parts that add new stuff from the Core rules).
The document presents new rules and concepts introduced in the Core rules. To its credit, it says (or implies, at least) that adding these additional rules is optional, with phrases like “…if you choose to add blah blah…” However, in practice I think it would require a fair amount of work to transition to the Core rules without including everything. Maybe you could drop stuff like Attacks of Opportunity or Combat Manuevers (though doing so would render many Core feats and class abilities moot), but the more complex spell and monsters descriptions in the Core rules require a lot more work to BB-iffy.
The Transitions document also details some low level Pathfinder adventures appropriate for use with the BB, with notes on how to read one of them, the free module Master of the Fallen Fortress, for a BB game. This section is somewhat more useful for someone staying with the BB, but the conversion notes are nothing that you couldn’t have figured out on your own anyways.
If you’ve been playing the BB for a while and you’d like to transition to the crunchier, more complex, Pathfinder Core rules, you’ll probably find this document to be of great use. If you plan on sticking with the BB, you should still still give it a look over, at the very least for the information on raising characters to 6th level.