Burlington is an excellent place and it offes something for everyone. I was nearly living about 2 years in Burlington for business purpose and visited many places all around. It maybe worth starting from Burlington's waterfront since it offers hiking and riding trails, educational camps for kids, outdoor concerts and swinging benches. Take a tour of harbor and explore the beauty of Burlington.
Rent a bike or walk along Lake Champlain for a few miles and have lunch at any one of the Burlington Bay Cafe overlooking the waterfront. Experience the delicious Vermont’s finest pure Vermont maple syrup, mouthwatering cob-smoked meats, cheddar cheese and other special foods. Take a little rest then rent a canoe or boat and explore the beauty of Burlington.
Hike around the top of Mt. Mansfield and view the nature. Visit the Vermont Teddy Bear Company and take an informative 30 mins tour revealing the magic of hand crafting teddy bears and watch teddy bears come to life before your eyes.
Visit Lake Champlain Chocolates,a choclate factory open for visitors and free sampling. Also visit the ECHO at the Leahy Center for Lake Champlain, a combination aquarium and science center where children can see a 2,750-gallon aquarium, visit FrogWorld as well and explore the world of dinosaurs.
Hope this will help to plan for your 5 days trip, have fun.