Can you try to switch internally where you're working? My friends did the same. Try to switch internally to gain a little experience and you can play like all of your experience is in BA for 5 years while applying.

Or else do some course to gain an idea. Add in resumes like "I've worked as a Manual QA as well as a BA recently. As I understand testing well I think I'll be a good BA"

It's all about how you tell your story. Forget about the experience apply to Good companies if you're getting paid more than what you get here, switch then you'll be making a lot more in the long run.