K.,
My oldest stopped napping on a regular basis just before her 5th birthday. We still had quiet time for 1-1 1/2 hours until she left for Kindergarten. We lived in a state where every class had all day Kindergarten, so she had rest time there but rarely fell asleep. Now she is 7, has quiet time with a chapter book for 1 hour and falls asleep 1-2 times per month.
My second oldest is 5 1/2 and still naps every day for at least 1- 1 1/2 hours. My 3 year old still naps for 2-3 hours every day.
With my 5 year old who doesn't want to nap anymore but really needs it, I do the same thing I did when I taught preschool. I tell him that he doesn't have to fall asleep, but he does have to lie still and close his eyes for 2 hours. Kids keep themselves awake because they keep themselves active. If they have to hold still and keep their eyes closed, they will fall asleep.
Be persistent with the naps. It is worth it to have a happy, well rested child.
Good luck,
S.