My interview is exactly one day after my 5-year PR anniversary. I don't think you should worry or cancel the interview, just go and ask the IO if that is a problem. In addition, even if you have your initial interview before your eligibility starts, you might have your oath ceremony after so that shouldn't be a problem.
Interview is just a week before eligibility date, so oath would be after eligibility date for sure. I couldn't find any law or internal USCIS instruction on internet that says that interview should be conducted before eligibility date. The law says that one can't be granted citizenship before eligibility date, but that's it.