I think part of the reason she is waking at 5 am is because she is overtired. And yes, crawling and teething definitely affect naps!
In order to not reinforce the early wakings and short naps, you ideally want that first nap not to start until 9am. But don't extend it all at once - I'd try 8am for 3 days, then 8:15 for 3, then 8:30 for three, etc. Ideally she'd sleep from 9-10:30. Then you want second nap to start between 1:30 and 2 - and you can let her sleep a full 2 hours if she can/will. At her age she should definitely be able to handle 3 hours A time (my DD is 9 months and one week and goes between 3-3.5 hours awake).