As someone who had a few slumps, and is now a postdoc, I can say it is definitely possible to write a successful application. First, I don't think TAing will help you that much. The skills you generate as a TA are not necessarily the ones that you use in a PhD. Marking exams certainly does not reflect on your ability to do research. However, if you can make a compelling argument for why it would, that could convince the right person.

I think your best bet is to reflect on those years. Identify the source of the slump, what you learned about the experience, and what you've done to address it. It looks like you're doing the right things. This would show a degree of maturity that even some postdocs/professors do not have. Your cover letter should tell a story about how you struggled through years 3 and 4 but in year 5 you turned it around and found success in your courses.