I'm surprised that they would ask you
to write the letter, rather than have you get one from a licensed mental health professional attesting to your ability to practice safely; they usually want to know about your current mental state, compliance with medication/therapy and so on.
Since you yourself are writing the statement, you want acknowledge the fact that you do have a mental condition (honesty is ALWAYS the best policy when you get cornered with something like this), then describe what you are doing about it and how your treatment is keeping you stable. Focus on the POSITIVE, not how your condition "could" affect your practice; if you've made it through 5 years of school, you must be doing something right, and you need to state that for the record.
TBH, I haven't had to deal with anything like this yet, but I have to renew my license in January and am figuring on using the same approach, since I'll have to disclose the mental health diagnosis I picked up last winter and am being treated for. LMK how it works out for you......I really don't think you have that much to worry about, if they denied licenses to all the nurses who have depression and/or anxiety, there'd be no one left to take care of the patients.