My wife and I were in Parma for 4 nights about one month ago. We did a private food tour from Parma arranged by Laura Panella. Google her name and foodtours.it. The tour included pick up, drop off, lunch and visits to producers of Parmesan, Prosciutto and Balsamic Vinegar. Tour was from about 9am - 3pm. There were just the two of us, though, so not sure if they have vehicles large enough for five (you would need to check). I think I originally found Laura's name from other posters on this forum. Another option would be to hire a private guide who could separately line up a private driver for touring. We hired a private guide named Nathalie Zaveroni in Bologna for two separate walking tours and she also does tours in Parma. Nathalie was wonderful! She has contacts with a driver in Parma who she could possibly collaborate with and she may be able to provide you a quote for a food tour. Check out her website. As a third option, check with your hotel, they might have trusted guides they suggest.
In Parma we had a nice dinner at Restaurant Gallo D Oro, which was suggested by our hotel when we were looking for an early dinner. They opened at around 5:00pm (we found that most restaurants did not open until 7:00pm). We had a very nice lunch at Restaurant Angiol D'Or. For great take out sandwiches we really liked Pepen, which had a wide variety of delicious sandwiches. I think they are open for lunch and early evening. We also had wine and snacks at wine bar Tabarro.