S., I also have a finicky 5 yr old. My doctor said Pedia sure was fine as long as it was only given in small amount. Of course trying to get the good food in was mandatory. But our doctor wasn't too worried. My daughter amazingly taste everything I make. She may not like and will nay many things, but try she will.
I started involving my daughter in the grocery shopping. She gets to suggest a menu for one or two nights meals. She helps make the list of only healthy foods(school has helped with this mind set). She is allowed one special treat which sometimes surprises me and is healthy. She goes shopping with me as long as she behaves. My five year old sometimes wonders. She loves to weigh everything in the produce department. It becames a learning experience as well. I am usually tired afterwards but it slowly and gradually is getting better.
We eat a lot quesadilla's(spelling), hotdogs(chicken or turkey), sandwiches, sausages, carrots, cucumbers, corn, artichokes, lettuce, asian foods, pizza(homemade and special frozen), meatballs from trader joes. I think with time and taste testing they will learn to love certain foods. I hated broccoli until I was 25 and now I can't be without it. Hang in there you will figure it out.